id	sid	tid	token	lemma	pos
ejpam-5208	1	1	european	european	PROPN
ejpam-5208	1	2	journal	journal	PROPN
ejpam-5208	1	3	of	of	ADP
ejpam-5208	1	4	pure	pure	ADJ
ejpam-5208	1	5	and	and	CCONJ
ejpam-5208	1	6	applied	apply	VERB
ejpam-5208	1	7	mathematics	mathematic	NOUN
ejpam-5208	1	8	vol	vol	NOUN
ejpam-5208	1	9	.	.	PROPN
ejpam-5208	2	1	17	17	NUM
ejpam-5208	2	2	,	,	PUNCT
ejpam-5208	2	3	no	no	INTJ
ejpam-5208	2	4	.	.	NOUN
ejpam-5208	2	5	3	3	NUM
ejpam-5208	2	6	,	,	PUNCT
ejpam-5208	2	7	2024	2024	NUM
ejpam-5208	2	8	,	,	PUNCT
ejpam-5208	2	9	2173	2173	NUM
ejpam-5208	2	10	-	-	SYM
ejpam-5208	2	11	2181	2181	NUM
ejpam-5208	2	12	issn	issn	PROPN
ejpam-5208	2	13	1307	1307	NUM
ejpam-5208	2	14	-	-	SYM
ejpam-5208	2	15	5543	5543	NUM
ejpam-5208	2	16	–	–	PUNCT
ejpam-5208	2	17	ejpam.com	ejpam.com	X
ejpam-5208	2	18	published	publish	VERB
ejpam-5208	2	19	by	by	ADP
ejpam-5208	2	20	new	new	PROPN
ejpam-5208	2	21	york	york	PROPN
ejpam-5208	2	22	business	business	PROPN
ejpam-5208	2	23	global	global	PROPN
ejpam-5208	2	24	on	on	ADP
ejpam-5208	2	25	ψgs	ψgs	NOUN
ejpam-5208	2	26	-	-	PUNCT
ejpam-5208	2	27	functions	function	NOUN
ejpam-5208	2	28	in	in	ADP
ejpam-5208	2	29	bitopological	bitopological	ADJ
ejpam-5208	2	30	spaces	space	NOUN
ejpam-5208	2	31	lezel	lezel	ADJ
ejpam-5208	2	32	mernilo	mernilo	PROPN
ejpam-5208	2	33	tutanes	tutane	NOUN
ejpam-5208	2	34	department	department	PROPN
ejpam-5208	2	35	of	of	ADP
ejpam-5208	2	36	mathematics	mathematics	PROPN
ejpam-5208	2	37	,	,	PUNCT
ejpam-5208	2	38	college	college	NOUN
ejpam-5208	2	39	of	of	ADP
ejpam-5208	2	40	arts	art	NOUN
ejpam-5208	2	41	and	and	CCONJ
ejpam-5208	2	42	sciences	sciences	PROPN
ejpam-5208	2	43	,	,	PUNCT
ejpam-5208	2	44	bukidnon	bukidnon	NOUN
ejpam-5208	2	45	state	state	PROPN
ejpam-5208	2	46	university	university	PROPN
ejpam-5208	2	47	,	,	PUNCT
ejpam-5208	2	48	malaybalay	malaybalay	NOUN
ejpam-5208	2	49	city	city	NOUN
ejpam-5208	2	50	,	,	PUNCT
ejpam-5208	2	51	bukidnon	bukidnon	NOUN
ejpam-5208	2	52	,	,	PUNCT
ejpam-5208	3	1	philippines	philippine	NOUN
ejpam-5208	3	2	abstract	abstract	ADJ
ejpam-5208	3	3	.	.	PUNCT
ejpam-5208	4	1	a	a	DET
ejpam-5208	4	2	subset	subset	NOUN
ejpam-5208	4	3	a	a	PRON
ejpam-5208	4	4	of	of	ADP
ejpam-5208	4	5	a	a	DET
ejpam-5208	4	6	bitopological	bitopological	ADJ
ejpam-5208	4	7	space	space	NOUN
ejpam-5208	4	8	(	(	PUNCT
ejpam-5208	4	9	x	x	NOUN
ejpam-5208	4	10	,	,	PUNCT
ejpam-5208	4	11	τ1	τ1	NOUN
ejpam-5208	4	12	,	,	PUNCT
ejpam-5208	4	13	τ2	τ2	NOUN
ejpam-5208	4	14	)	)	PUNCT
ejpam-5208	4	15	is	be	AUX
ejpam-5208	4	16	called	call	VERB
ejpam-5208	4	17	an	an	DET
ejpam-5208	4	18	(	(	PUNCT
ejpam-5208	4	19	i	i	NOUN
ejpam-5208	4	20	,	,	PUNCT
ejpam-5208	4	21	j)-ψgs	j)-ψgs	ADV
ejpam-5208	4	22	-	-	PUNCT
ejpam-5208	4	23	closed	closed	ADJ
ejpam-5208	4	24	set	set	NOUN
ejpam-5208	4	25	if	if	SCONJ
ejpam-5208	4	26	(	(	PUNCT
ejpam-5208	4	27	i	i	NOUN
ejpam-5208	4	28	,	,	PUNCT
ejpam-5208	4	29	j)-ψcl(a	j)-ψcl(a	PROPN
ejpam-5208	4	30	)	)	PUNCT
ejpam-5208	4	31	⊆	⊆	NUM
ejpam-5208	4	32	u	u	NOUN
ejpam-5208	4	33	whenever	whenever	SCONJ
ejpam-5208	4	34	a	a	DET
ejpam-5208	4	35	⊆	⊆	NUM
ejpam-5208	4	36	u	u	NOUN
ejpam-5208	4	37	,	,	PUNCT
ejpam-5208	4	38	u	u	NOUN
ejpam-5208	4	39	is	be	AUX
ejpam-5208	4	40	(	(	PUNCT
ejpam-5208	4	41	i	i	PROPN
ejpam-5208	4	42	,	,	PUNCT
ejpam-5208	4	43	j)-semi	j)-semi	NOUN
ejpam-5208	4	44	-	-	PUNCT
ejpam-5208	4	45	open	open	ADJ
ejpam-5208	4	46	in	in	ADP
ejpam-5208	4	47	(	(	PUNCT
ejpam-5208	4	48	x	x	NOUN
ejpam-5208	4	49	,	,	PUNCT
ejpam-5208	4	50	τ1	τ1	NOUN
ejpam-5208	4	51	,	,	PUNCT
ejpam-5208	4	52	τ2	τ2	NOUN
ejpam-5208	4	53	)	)	PUNCT
ejpam-5208	4	54	.	.	PUNCT
ejpam-5208	5	1	in	in	ADP
ejpam-5208	5	2	this	this	DET
ejpam-5208	5	3	work	work	NOUN
ejpam-5208	5	4	,	,	PUNCT
ejpam-5208	5	5	the	the	DET
ejpam-5208	5	6	properties	property	NOUN
ejpam-5208	5	7	of	of	ADP
ejpam-5208	5	8	this	this	DET
ejpam-5208	5	9	set	set	NOUN
ejpam-5208	5	10	are	be	AUX
ejpam-5208	5	11	considered	consider	VERB
ejpam-5208	5	12	to	to	PART
ejpam-5208	5	13	investigate	investigate	VERB
ejpam-5208	5	14	the	the	DET
ejpam-5208	5	15	concepts	concept	NOUN
ejpam-5208	5	16	of	of	ADP
ejpam-5208	5	17	ψgs	ψgs	NOUN
ejpam-5208	5	18	-	-	PUNCT
ejpam-5208	5	19	functions	function	NOUN
ejpam-5208	5	20	in	in	ADP
ejpam-5208	5	21	bitopological	bitopological	ADJ
ejpam-5208	5	22	spaces	space	NOUN
ejpam-5208	5	23	.	.	PUNCT
ejpam-5208	6	1	specifically	specifically	ADV
ejpam-5208	6	2	,	,	PUNCT
ejpam-5208	6	3	this	this	DET
ejpam-5208	6	4	study	study	NOUN
ejpam-5208	6	5	establishes	establish	VERB
ejpam-5208	6	6	some	some	DET
ejpam-5208	6	7	properties	property	NOUN
ejpam-5208	6	8	and	and	CCONJ
ejpam-5208	6	9	provides	provide	VERB
ejpam-5208	6	10	characterizations	characterization	NOUN
ejpam-5208	6	11	of	of	ADP
ejpam-5208	6	12	ψgs	ψgs	ADV
ejpam-5208	6	13	-	-	PUNCT
ejpam-5208	6	14	open	open	ADJ
ejpam-5208	6	15	and	and	CCONJ
ejpam-5208	6	16	ψgs	ψgs	ADV
ejpam-5208	6	17	-	-	PUNCT
ejpam-5208	6	18	closed	close	VERB
ejpam-5208	6	19	functions	function	NOUN
ejpam-5208	6	20	,	,	PUNCT
ejpam-5208	6	21	ψgs	ψgs	ADV
ejpam-5208	6	22	-	-	PUNCT
ejpam-5208	6	23	continuous	continuous	ADJ
ejpam-5208	6	24	functions	function	NOUN
ejpam-5208	6	25	,	,	PUNCT
ejpam-5208	6	26	and	and	CCONJ
ejpam-5208	6	27	ψgs	ψgs	ADV
ejpam-5208	6	28	-	-	PUNCT
ejpam-5208	6	29	irresolute	irresolute	ADJ
ejpam-5208	6	30	functions	function	NOUN
ejpam-5208	6	31	in	in	ADP
ejpam-5208	6	32	bitopological	bitopological	ADJ
ejpam-5208	6	33	spaces	space	NOUN
ejpam-5208	6	34	.	.	PUNCT
ejpam-5208	7	1	2020	2020	NUM
ejpam-5208	7	2	mathematics	mathematic	NOUN
ejpam-5208	7	3	subject	subject	NOUN
ejpam-5208	7	4	classifications	classification	NOUN
ejpam-5208	7	5	:	:	PUNCT
ejpam-5208	7	6	18f60	18f60	NUM
ejpam-5208	7	7	,	,	PUNCT
ejpam-5208	7	8	05c69	05c69	NUM
ejpam-5208	7	9	,	,	PUNCT
ejpam-5208	7	10	30h80	30h80	NUM
ejpam-5208	7	11	key	key	ADJ
ejpam-5208	7	12	words	word	NOUN
ejpam-5208	7	13	and	and	CCONJ
ejpam-5208	7	14	phrases	phrase	NOUN
ejpam-5208	7	15	:	:	PUNCT
ejpam-5208	7	16	bitopological	bitopological	ADJ
ejpam-5208	7	17	spaces	space	NOUN
ejpam-5208	7	18	,	,	PUNCT
ejpam-5208	7	19	ψgs	ψgs	ADV
ejpam-5208	7	20	-	-	PUNCT
ejpam-5208	7	21	closed	close	VERB
ejpam-5208	7	22	set	set	NOUN
ejpam-5208	7	23	,	,	PUNCT
ejpam-5208	7	24	ψgs	ψgs	ADV
ejpam-5208	7	25	-	-	PUNCT
ejpam-5208	7	26	open	open	ADJ
ejpam-5208	7	27	function	function	NOUN
ejpam-5208	7	28	,	,	PUNCT
ejpam-5208	7	29	ψgs	ψgs	ADV
ejpam-5208	7	30	-	-	PUNCT
ejpam-5208	7	31	closed	close	VERB
ejpam-5208	7	32	function	function	NOUN
ejpam-5208	7	33	,	,	PUNCT
ejpam-5208	7	34	ψgs	ψgs	ADV
ejpam-5208	7	35	-	-	PUNCT
ejpam-5208	7	36	continuous	continuous	ADJ
ejpam-5208	7	37	function	function	NOUN
ejpam-5208	7	38	,	,	PUNCT
ejpam-5208	7	39	ψgs	ψgs	ADV
ejpam-5208	7	40	-	-	PUNCT
ejpam-5208	7	41	irresolute	irresolute	ADJ
ejpam-5208	7	42	function	function	NOUN
ejpam-5208	7	43	1	1	NUM
ejpam-5208	7	44	.	.	PUNCT
ejpam-5208	8	1	introduction	introduction	NOUN
ejpam-5208	8	2	topology	topology	NOUN
ejpam-5208	8	3	is	be	AUX
ejpam-5208	8	4	a	a	DET
ejpam-5208	8	5	branch	branch	NOUN
ejpam-5208	8	6	of	of	ADP
ejpam-5208	8	7	mathematics	mathematic	NOUN
ejpam-5208	8	8	that	that	PRON
ejpam-5208	8	9	studies	study	VERB
ejpam-5208	8	10	geometric	geometric	ADJ
ejpam-5208	8	11	properties	property	NOUN
ejpam-5208	8	12	and	and	CCONJ
ejpam-5208	8	13	spatial	spatial	ADJ
ejpam-5208	8	14	relations	relation	NOUN
ejpam-5208	8	15	unaffected	unaffected	ADJ
ejpam-5208	8	16	by	by	ADP
ejpam-5208	8	17	the	the	DET
ejpam-5208	8	18	continuous	continuous	ADJ
ejpam-5208	8	19	changes	change	NOUN
ejpam-5208	8	20	in	in	ADP
ejpam-5208	8	21	the	the	DET
ejpam-5208	8	22	shape	shape	NOUN
ejpam-5208	8	23	or	or	CCONJ
ejpam-5208	8	24	size	size	NOUN
ejpam-5208	8	25	of	of	ADP
ejpam-5208	8	26	objects	object	NOUN
ejpam-5208	8	27	.	.	PUNCT
ejpam-5208	9	1	a	a	DET
ejpam-5208	9	2	topological	topological	ADJ
ejpam-5208	9	3	space	space	NOUN
ejpam-5208	9	4	is	be	AUX
ejpam-5208	9	5	a	a	DET
ejpam-5208	9	6	set	set	NOUN
ejpam-5208	9	7	equipped	equip	VERB
ejpam-5208	9	8	with	with	ADP
ejpam-5208	9	9	a	a	DET
ejpam-5208	9	10	topology	topology	NOUN
ejpam-5208	9	11	,	,	PUNCT
ejpam-5208	9	12	which	which	PRON
ejpam-5208	9	13	is	be	AUX
ejpam-5208	9	14	a	a	DET
ejpam-5208	9	15	collection	collection	NOUN
ejpam-5208	9	16	of	of	ADP
ejpam-5208	9	17	open	open	ADJ
ejpam-5208	9	18	sets	set	NOUN
ejpam-5208	9	19	satisfying	satisfy	VERB
ejpam-5208	9	20	certain	certain	ADJ
ejpam-5208	9	21	axioms	axiom	NOUN
ejpam-5208	9	22	related	relate	VERB
ejpam-5208	9	23	to	to	ADP
ejpam-5208	9	24	union	union	NOUN
ejpam-5208	9	25	,	,	PUNCT
ejpam-5208	9	26	intersection	intersection	NOUN
ejpam-5208	9	27	,	,	PUNCT
ejpam-5208	9	28	and	and	CCONJ
ejpam-5208	9	29	inclusion	inclusion	NOUN
ejpam-5208	9	30	of	of	ADP
ejpam-5208	9	31	sets	set	NOUN
ejpam-5208	9	32	.	.	PUNCT
ejpam-5208	10	1	to	to	PART
ejpam-5208	10	2	deepen	deepen	VERB
ejpam-5208	10	3	the	the	DET
ejpam-5208	10	4	understanding	understanding	NOUN
ejpam-5208	10	5	and	and	CCONJ
ejpam-5208	10	6	extend	extend	VERB
ejpam-5208	10	7	the	the	DET
ejpam-5208	10	8	scope	scope	NOUN
ejpam-5208	10	9	of	of	ADP
ejpam-5208	10	10	topological	topological	ADJ
ejpam-5208	10	11	concepts	concept	NOUN
ejpam-5208	10	12	,	,	PUNCT
ejpam-5208	10	13	the	the	DET
ejpam-5208	10	14	notion	notion	NOUN
ejpam-5208	10	15	of	of	ADP
ejpam-5208	10	16	bitopological	bitopological	ADJ
ejpam-5208	10	17	spaces	space	NOUN
ejpam-5208	10	18	was	be	AUX
ejpam-5208	10	19	introduced	introduce	VERB
ejpam-5208	10	20	.	.	PUNCT
ejpam-5208	11	1	a	a	DET
ejpam-5208	11	2	bitopological	bitopological	ADJ
ejpam-5208	11	3	space	space	NOUN
ejpam-5208	11	4	is	be	AUX
ejpam-5208	11	5	a	a	DET
ejpam-5208	11	6	generalization	generalization	NOUN
ejpam-5208	11	7	of	of	ADP
ejpam-5208	11	8	topological	topological	ADJ
ejpam-5208	11	9	spaces	space	NOUN
ejpam-5208	11	10	,	,	PUNCT
ejpam-5208	11	11	where	where	SCONJ
ejpam-5208	11	12	two	two	NUM
ejpam-5208	11	13	different	different	ADJ
ejpam-5208	11	14	topologies	topology	NOUN
ejpam-5208	11	15	are	be	AUX
ejpam-5208	11	16	defined	define	VERB
ejpam-5208	11	17	on	on	ADP
ejpam-5208	11	18	the	the	DET
ejpam-5208	11	19	same	same	ADJ
ejpam-5208	11	20	underlying	underlying	ADJ
ejpam-5208	11	21	set	set	NOUN
ejpam-5208	11	22	.	.	PUNCT
ejpam-5208	12	1	for	for	ADP
ejpam-5208	12	2	instance	instance	NOUN
ejpam-5208	12	3	,	,	PUNCT
ejpam-5208	12	4	(	(	PUNCT
ejpam-5208	12	5	x	x	NOUN
ejpam-5208	12	6	,	,	PUNCT
ejpam-5208	12	7	τ1	τ1	NOUN
ejpam-5208	12	8	,	,	PUNCT
ejpam-5208	12	9	τ2	τ2	NOUN
ejpam-5208	12	10	)	)	PUNCT
ejpam-5208	12	11	is	be	AUX
ejpam-5208	12	12	a	a	DET
ejpam-5208	12	13	bitopological	bitopological	ADJ
ejpam-5208	12	14	space	space	NOUN
ejpam-5208	12	15	where	where	SCONJ
ejpam-5208	12	16	x	x	PRON
ejpam-5208	12	17	is	be	AUX
ejpam-5208	12	18	a	a	DET
ejpam-5208	12	19	nonempty	nonempty	ADV
ejpam-5208	12	20	set	set	VERB
ejpam-5208	12	21	and	and	CCONJ
ejpam-5208	12	22	τ1	τ1	NOUN
ejpam-5208	12	23	and	and	CCONJ
ejpam-5208	12	24	τ2	τ2	NOUN
ejpam-5208	12	25	are	be	AUX
ejpam-5208	12	26	two	two	NUM
ejpam-5208	12	27	different	different	ADJ
ejpam-5208	12	28	topologies	topology	NOUN
ejpam-5208	12	29	.	.	PUNCT
ejpam-5208	13	1	many	many	ADJ
ejpam-5208	13	2	concepts	concept	NOUN
ejpam-5208	13	3	have	have	AUX
ejpam-5208	13	4	been	be	AUX
ejpam-5208	13	5	investigated	investigate	VERB
ejpam-5208	13	6	in	in	ADP
ejpam-5208	13	7	bitopological	bitopological	ADJ
ejpam-5208	13	8	spaces	space	NOUN
ejpam-5208	13	9	.	.	PUNCT
ejpam-5208	14	1	one	one	NUM
ejpam-5208	14	2	of	of	ADP
ejpam-5208	14	3	these	these	PRON
ejpam-5208	14	4	is	be	AUX
ejpam-5208	14	5	the	the	DET
ejpam-5208	14	6	concept	concept	NOUN
ejpam-5208	14	7	of	of	ADP
ejpam-5208	14	8	functions	function	NOUN
ejpam-5208	14	9	.	.	PUNCT
ejpam-5208	15	1	functions	function	NOUN
ejpam-5208	15	2	in	in	ADP
ejpam-5208	15	3	bitopological	bitopological	ADJ
ejpam-5208	15	4	spaces	space	NOUN
ejpam-5208	15	5	refer	refer	VERB
ejpam-5208	15	6	to	to	ADP
ejpam-5208	15	7	the	the	DET
ejpam-5208	15	8	mappings	mapping	NOUN
ejpam-5208	15	9	between	between	ADP
ejpam-5208	15	10	two	two	NUM
ejpam-5208	15	11	bitopological	bitopological	ADJ
ejpam-5208	15	12	spaces	space	NOUN
ejpam-5208	15	13	.	.	PUNCT
ejpam-5208	16	1	for	for	ADP
ejpam-5208	16	2	instance	instance	NOUN
ejpam-5208	16	3	,	,	PUNCT
ejpam-5208	16	4	f	f	X
ejpam-5208	16	5	:	:	PUNCT
ejpam-5208	16	6	(	(	PUNCT
ejpam-5208	16	7	x	x	NOUN
ejpam-5208	16	8	,	,	PUNCT
ejpam-5208	16	9	τ1	τ1	NOUN
ejpam-5208	16	10	,	,	PUNCT
ejpam-5208	16	11	τ2	τ2	NOUN
ejpam-5208	16	12	)	)	PUNCT
ejpam-5208	16	13	→	→	SYM
ejpam-5208	16	14	(	(	PUNCT
ejpam-5208	16	15	y	y	PROPN
ejpam-5208	16	16	,	,	PUNCT
ejpam-5208	16	17	σ1	σ1	PROPN
ejpam-5208	16	18	,	,	PUNCT
ejpam-5208	16	19	σ2	σ2	PROPN
ejpam-5208	16	20	)	)	PUNCT
ejpam-5208	16	21	is	be	AUX
ejpam-5208	16	22	a	a	DET
ejpam-5208	16	23	function	function	NOUN
ejpam-5208	16	24	in	in	ADP
ejpam-5208	16	25	bitopological	bitopological	ADJ
ejpam-5208	16	26	spaces	space	NOUN
ejpam-5208	16	27	where	where	SCONJ
ejpam-5208	16	28	(	(	PUNCT
ejpam-5208	16	29	x	x	NOUN
ejpam-5208	16	30	,	,	PUNCT
ejpam-5208	16	31	τ1	τ1	NOUN
ejpam-5208	16	32	,	,	PUNCT
ejpam-5208	16	33	τ2	τ2	NOUN
ejpam-5208	16	34	)	)	PUNCT
ejpam-5208	16	35	and	and	CCONJ
ejpam-5208	16	36	(	(	PUNCT
ejpam-5208	16	37	y	y	PROPN
ejpam-5208	16	38	,	,	PUNCT
ejpam-5208	16	39	σ1	σ1	PROPN
ejpam-5208	16	40	,	,	PUNCT
ejpam-5208	16	41	σ2	σ2	PROPN
ejpam-5208	16	42	)	)	PUNCT
ejpam-5208	16	43	are	be	AUX
ejpam-5208	16	44	two	two	NUM
ejpam-5208	16	45	bitopological	bitopological	ADJ
ejpam-5208	16	46	spaces	space	NOUN
ejpam-5208	16	47	.	.	PUNCT
ejpam-5208	17	1	important	important	ADJ
ejpam-5208	17	2	functions	function	NOUN
ejpam-5208	17	3	in	in	ADP
ejpam-5208	17	4	bitopological	bitopological	ADJ
ejpam-5208	17	5	spaces	space	NOUN
ejpam-5208	17	6	include	include	VERB
ejpam-5208	17	7	open	open	ADJ
ejpam-5208	17	8	and	and	CCONJ
ejpam-5208	17	9	closed	closed	ADJ
ejpam-5208	17	10	functions	function	NOUN
ejpam-5208	17	11	,	,	PUNCT
ejpam-5208	17	12	continuous	continuous	ADJ
ejpam-5208	17	13	functions	function	NOUN
ejpam-5208	17	14	,	,	PUNCT
ejpam-5208	17	15	and	and	CCONJ
ejpam-5208	17	16	irresolute	irresolute	ADJ
ejpam-5208	17	17	functions	function	NOUN
ejpam-5208	17	18	.	.	PUNCT
ejpam-5208	18	1	over	over	ADP
ejpam-5208	18	2	the	the	DET
ejpam-5208	18	3	years	year	NOUN
ejpam-5208	18	4	,	,	PUNCT
ejpam-5208	18	5	many	many	ADJ
ejpam-5208	18	6	researchers	researcher	NOUN
ejpam-5208	18	7	have	have	AUX
ejpam-5208	18	8	introduced	introduce	VERB
ejpam-5208	18	9	different	different	ADJ
ejpam-5208	18	10	types	type	NOUN
ejpam-5208	18	11	of	of	ADP
ejpam-5208	18	12	functions	function	NOUN
ejpam-5208	18	13	in	in	ADP
ejpam-5208	18	14	bitopological	bitopological	ADJ
ejpam-5208	18	15	spaces	space	NOUN
ejpam-5208	18	16	.	.	PUNCT
ejpam-5208	19	1	noiri	noiri	PROPN
ejpam-5208	19	2	and	and	CCONJ
ejpam-5208	19	3	popa	popa	NOUN
ejpam-5208	19	4	in	in	ADP
ejpam-5208	19	5	[	[	X
ejpam-5208	19	6	7	7	NUM
ejpam-5208	19	7	]	]	PUNCT
ejpam-5208	19	8	studied	study	VERB
ejpam-5208	19	9	some	some	DET
ejpam-5208	19	10	properties	property	NOUN
ejpam-5208	19	11	of	of	ADP
ejpam-5208	19	12	weakly	weakly	ADJ
ejpam-5208	19	13	open	open	ADJ
ejpam-5208	19	14	functions	function	NOUN
ejpam-5208	19	15	in	in	ADP
ejpam-5208	19	16	doi	doi	NOUN
ejpam-5208	19	17	:	:	PUNCT
ejpam-5208	19	18	https://doi.org/10.29020/nybg.ejpam.v17i3.5208	https://doi.org/10.29020/nybg.ejpam.v17i3.5208	ADJ
ejpam-5208	19	19	email	email	NOUN
ejpam-5208	19	20	address	address	NOUN
ejpam-5208	19	21	:	:	PUNCT
ejpam-5208	19	22	lezeltutanes@buksu.edu.ph	lezeltutanes@buksu.edu.ph	PROPN
ejpam-5208	19	23	(	(	PUNCT
ejpam-5208	19	24	l.m	l.m	PROPN
ejpam-5208	19	25	.	.	PROPN
ejpam-5208	19	26	tutanes	tutane	NOUN
ejpam-5208	19	27	)	)	PUNCT
ejpam-5208	19	28	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5208	19	29	2173	2173	NUM
ejpam-5208	20	1	©	©	ADP
ejpam-5208	20	2	2024	2024	NUM
ejpam-5208	20	3	ejpam	ejpam	NOUN
ejpam-5208	20	4	all	all	DET
ejpam-5208	20	5	rights	right	NOUN
ejpam-5208	20	6	reserved	reserve	VERB
ejpam-5208	20	7	.	.	PUNCT
ejpam-5208	21	1	l.	l.	PROPN
ejpam-5208	21	2	m.	m.	PROPN
ejpam-5208	21	3	tutanes	tutane	NOUN
ejpam-5208	21	4	/	/	SYM
ejpam-5208	21	5	eur	eur	PROPN
ejpam-5208	21	6	.	.	PUNCT
ejpam-5208	22	1	j.	j.	PROPN
ejpam-5208	22	2	pure	pure	PROPN
ejpam-5208	22	3	appl	appl	PROPN
ejpam-5208	22	4	.	.	PROPN
ejpam-5208	22	5	math	math	PROPN
ejpam-5208	22	6	,	,	PUNCT
ejpam-5208	22	7	17	17	NUM
ejpam-5208	22	8	(	(	PUNCT
ejpam-5208	22	9	3	3	NUM
ejpam-5208	22	10	)	)	PUNCT
ejpam-5208	22	11	(	(	PUNCT
ejpam-5208	22	12	2024	2024	NUM
ejpam-5208	22	13	)	)	PUNCT
ejpam-5208	22	14	,	,	PUNCT
ejpam-5208	22	15	2173	2173	NUM
ejpam-5208	22	16	-	-	SYM
ejpam-5208	22	17	2181	2181	NUM
ejpam-5208	22	18	2174	2174	NUM
ejpam-5208	22	19	bitopological	bitopological	ADJ
ejpam-5208	22	20	spaces	space	NOUN
ejpam-5208	22	21	and	and	CCONJ
ejpam-5208	22	22	obtained	obtain	VERB
ejpam-5208	22	23	further	further	ADJ
ejpam-5208	22	24	characterizations	characterization	NOUN
ejpam-5208	22	25	.	.	PUNCT
ejpam-5208	23	1	subsequently	subsequently	ADV
ejpam-5208	23	2	,	,	PUNCT
ejpam-5208	23	3	the	the	DET
ejpam-5208	23	4	properties	property	NOUN
ejpam-5208	23	5	and	and	CCONJ
ejpam-5208	23	6	characterizations	characterization	NOUN
ejpam-5208	23	7	of	of	ADP
ejpam-5208	23	8	weakly	weakly	ADJ
ejpam-5208	23	9	β	β	ADJ
ejpam-5208	23	10	-	-	ADJ
ejpam-5208	23	11	continuous	continuous	ADJ
ejpam-5208	23	12	functions	function	NOUN
ejpam-5208	23	13	in	in	ADP
ejpam-5208	23	14	bitopological	bitopological	ADJ
ejpam-5208	23	15	spaces	space	NOUN
ejpam-5208	23	16	were	be	AUX
ejpam-5208	23	17	investigated	investigate	VERB
ejpam-5208	23	18	by	by	ADP
ejpam-5208	23	19	tahiliani	tahiliani	NOUN
ejpam-5208	24	1	[	[	X
ejpam-5208	24	2	10	10	NUM
ejpam-5208	24	3	]	]	PUNCT
ejpam-5208	24	4	.	.	PUNCT
ejpam-5208	25	1	in	in	ADP
ejpam-5208	25	2	2012	2012	NUM
ejpam-5208	25	3	,	,	PUNCT
ejpam-5208	25	4	mukundhan	mukundhan	NOUN
ejpam-5208	25	5	and	and	CCONJ
ejpam-5208	25	6	nagaveni	nagaveni	ADJ
ejpam-5208	25	7	in	in	ADP
ejpam-5208	25	8	[	[	X
ejpam-5208	25	9	6	6	NUM
ejpam-5208	25	10	]	]	PUNCT
ejpam-5208	25	11	introduced	introduce	VERB
ejpam-5208	25	12	and	and	CCONJ
ejpam-5208	25	13	studied	study	VERB
ejpam-5208	25	14	two	two	NUM
ejpam-5208	25	15	new	new	ADJ
ejpam-5208	25	16	types	type	NOUN
ejpam-5208	25	17	of	of	ADP
ejpam-5208	25	18	functions	function	NOUN
ejpam-5208	25	19	in	in	ADP
ejpam-5208	25	20	bitopological	bitopological	ADJ
ejpam-5208	25	21	spaces	space	NOUN
ejpam-5208	25	22	called	call	VERB
ejpam-5208	25	23	(	(	PUNCT
ejpam-5208	25	24	i	i	PROPN
ejpam-5208	25	25	,	,	PUNCT
ejpam-5208	25	26	j)-quasi	j)-quasi	PRON
ejpam-5208	25	27	semi	semi	ADJ
ejpam-5208	25	28	weakly	weakly	ADV
ejpam-5208	25	29	g∗-open	g∗-open	ADJ
ejpam-5208	25	30	and	and	CCONJ
ejpam-5208	25	31	(	(	PUNCT
ejpam-5208	25	32	i	i	NOUN
ejpam-5208	25	33	,	,	PUNCT
ejpam-5208	25	34	j)-quasi	j)-quasi	DET
ejpam-5208	25	35	semi	semi	ADJ
ejpam-5208	25	36	weakly	weakly	ADV
ejpam-5208	25	37	g∗-closed	g∗-close	VERB
ejpam-5208	25	38	functions	function	NOUN
ejpam-5208	25	39	.	.	PUNCT
ejpam-5208	26	1	they	they	PRON
ejpam-5208	26	2	investigated	investigate	VERB
ejpam-5208	26	3	some	some	DET
ejpam-5208	26	4	properties	property	NOUN
ejpam-5208	26	5	and	and	CCONJ
ejpam-5208	26	6	proved	prove	VERB
ejpam-5208	26	7	equivalent	equivalent	ADJ
ejpam-5208	26	8	statements	statement	NOUN
ejpam-5208	26	9	.	.	PUNCT
ejpam-5208	27	1	in	in	ADP
ejpam-5208	27	2	the	the	DET
ejpam-5208	27	3	same	same	ADJ
ejpam-5208	27	4	year	year	NOUN
ejpam-5208	27	5	,	,	PUNCT
ejpam-5208	27	6	khedr	khedr	PROPN
ejpam-5208	27	7	and	and	CCONJ
ejpam-5208	27	8	al	al	PROPN
ejpam-5208	27	9	-	-	PUNCT
ejpam-5208	27	10	saadi	saadi	NOUN
ejpam-5208	27	11	in	in	ADP
ejpam-5208	27	12	[	[	X
ejpam-5208	27	13	3	3	NUM
ejpam-5208	27	14	]	]	PUNCT
ejpam-5208	27	15	introduced	introduce	VERB
ejpam-5208	27	16	and	and	CCONJ
ejpam-5208	27	17	investigated	investigate	VERB
ejpam-5208	27	18	the	the	DET
ejpam-5208	27	19	notions	notion	NOUN
ejpam-5208	27	20	of	of	ADP
ejpam-5208	27	21	a	a	DET
ejpam-5208	27	22	new	new	ADJ
ejpam-5208	27	23	class	class	NOUN
ejpam-5208	27	24	of	of	ADP
ejpam-5208	27	25	g	g	NOUN
ejpam-5208	27	26	-	-	PUNCT
ejpam-5208	27	27	closed	close	VERB
ejpam-5208	27	28	functions	function	NOUN
ejpam-5208	27	29	and	and	CCONJ
ejpam-5208	27	30	a	a	DET
ejpam-5208	27	31	class	class	NOUN
ejpam-5208	27	32	of	of	ADP
ejpam-5208	27	33	semigeneralized	semigeneralize	VERB
ejpam-5208	27	34	closed	close	VERB
ejpam-5208	27	35	functions	function	NOUN
ejpam-5208	27	36	in	in	ADP
ejpam-5208	27	37	bitopological	bitopological	ADJ
ejpam-5208	27	38	spaces	space	NOUN
ejpam-5208	27	39	.	.	PUNCT
ejpam-5208	28	1	they	they	PRON
ejpam-5208	28	2	further	far	ADV
ejpam-5208	28	3	studied	study	VERB
ejpam-5208	28	4	the	the	DET
ejpam-5208	28	5	properties	property	NOUN
ejpam-5208	28	6	of	of	ADP
ejpam-5208	28	7	generalized	generalized	ADJ
ejpam-5208	28	8	semi	semi	ADV
ejpam-5208	28	9	closed	closed	ADJ
ejpam-5208	28	10	and	and	CCONJ
ejpam-5208	28	11	semi	semi	ADJ
ejpam-5208	28	12	-	-	ADJ
ejpam-5208	28	13	generalized	generalized	ADJ
ejpam-5208	28	14	closed	closed	ADJ
ejpam-5208	28	15	functions	function	NOUN
ejpam-5208	28	16	in	in	ADP
ejpam-5208	28	17	bitopological	bitopological	ADJ
ejpam-5208	28	18	spaces	space	NOUN
ejpam-5208	28	19	.	.	PUNCT
ejpam-5208	29	1	in	in	ADP
ejpam-5208	29	2	2014	2014	NUM
ejpam-5208	29	3	,	,	PUNCT
ejpam-5208	29	4	mahmood	mahmood	PROPN
ejpam-5208	29	5	and	and	CCONJ
ejpam-5208	29	6	hamdi	hamdi	PROPN
ejpam-5208	29	7	in	in	ADP
ejpam-5208	29	8	[	[	X
ejpam-5208	29	9	4	4	NUM
ejpam-5208	29	10	]	]	PUNCT
ejpam-5208	29	11	created	create	VERB
ejpam-5208	29	12	a	a	DET
ejpam-5208	29	13	special	special	ADJ
ejpam-5208	29	14	type	type	NOUN
ejpam-5208	29	15	of	of	ADP
ejpam-5208	29	16	open	open	ADJ
ejpam-5208	29	17	and	and	CCONJ
ejpam-5208	29	18	closed	closed	ADJ
ejpam-5208	29	19	functions	function	NOUN
ejpam-5208	29	20	in	in	ADP
ejpam-5208	29	21	bitopological	bitopological	ADJ
ejpam-5208	29	22	spaces	space	NOUN
ejpam-5208	29	23	,	,	PUNCT
ejpam-5208	29	24	namely	namely	ADV
ejpam-5208	29	25	quasi	quasi	NOUN
ejpam-5208	29	26	(	(	PUNCT
ejpam-5208	29	27	1	1	NUM
ejpam-5208	29	28	,	,	PUNCT
ejpam-5208	29	29	2)∗	2)∗	NOUN
ejpam-5208	29	30	b	b	X
ejpam-5208	29	31	-	-	PUNCT
ejpam-5208	29	32	open	open	ADJ
ejpam-5208	29	33	functions	function	NOUN
ejpam-5208	29	34	and	and	CCONJ
ejpam-5208	29	35	quasi	quasi	ADJ
ejpam-5208	29	36	(	(	PUNCT
ejpam-5208	29	37	1	1	NUM
ejpam-5208	29	38	,	,	PUNCT
ejpam-5208	29	39	2)∗	2)∗	NOUN
ejpam-5208	29	40	b	b	X
ejpam-5208	29	41	-	-	PUNCT
ejpam-5208	29	42	closed	close	VERB
ejpam-5208	29	43	functions	function	NOUN
ejpam-5208	29	44	.	.	PUNCT
ejpam-5208	30	1	they	they	PRON
ejpam-5208	30	2	gave	give	VERB
ejpam-5208	30	3	some	some	DET
ejpam-5208	30	4	properties	property	NOUN
ejpam-5208	30	5	and	and	CCONJ
ejpam-5208	30	6	equivalent	equivalent	ADJ
ejpam-5208	30	7	statements	statement	NOUN
ejpam-5208	30	8	of	of	ADP
ejpam-5208	30	9	these	these	DET
ejpam-5208	30	10	concepts	concept	NOUN
ejpam-5208	30	11	.	.	PUNCT
ejpam-5208	31	1	in	in	ADP
ejpam-5208	31	2	2017	2017	NUM
ejpam-5208	31	3	,	,	PUNCT
ejpam-5208	31	4	sarma	sarma	PROPN
ejpam-5208	31	5	in	in	ADP
ejpam-5208	31	6	[	[	X
ejpam-5208	31	7	9	9	NUM
ejpam-5208	31	8	]	]	PUNCT
ejpam-5208	31	9	introduced	introduce	VERB
ejpam-5208	31	10	the	the	DET
ejpam-5208	31	11	notion	notion	NOUN
ejpam-5208	31	12	of	of	ADP
ejpam-5208	31	13	weakly	weakly	ADJ
ejpam-5208	31	14	b	b	X
ejpam-5208	31	15	-	-	PUNCT
ejpam-5208	31	16	open	open	ADJ
ejpam-5208	31	17	functions	function	NOUN
ejpam-5208	31	18	in	in	ADP
ejpam-5208	31	19	bitopological	bitopological	ADJ
ejpam-5208	31	20	spaces	space	NOUN
ejpam-5208	31	21	,	,	PUNCT
ejpam-5208	31	22	established	establish	VERB
ejpam-5208	31	23	some	some	DET
ejpam-5208	31	24	properties	property	NOUN
ejpam-5208	31	25	of	of	ADP
ejpam-5208	31	26	this	this	DET
ejpam-5208	31	27	function	function	NOUN
ejpam-5208	31	28	,	,	PUNCT
ejpam-5208	31	29	and	and	CCONJ
ejpam-5208	31	30	investigated	investigate	VERB
ejpam-5208	31	31	the	the	DET
ejpam-5208	31	32	relationships	relationship	NOUN
ejpam-5208	31	33	with	with	ADP
ejpam-5208	31	34	some	some	DET
ejpam-5208	31	35	other	other	ADJ
ejpam-5208	31	36	types	type	NOUN
ejpam-5208	31	37	of	of	ADP
ejpam-5208	31	38	spaces	space	NOUN
ejpam-5208	31	39	.	.	PUNCT
ejpam-5208	32	1	additionally	additionally	ADV
ejpam-5208	32	2	,	,	PUNCT
ejpam-5208	32	3	another	another	DET
ejpam-5208	32	4	type	type	NOUN
ejpam-5208	32	5	of	of	ADP
ejpam-5208	32	6	function	function	NOUN
ejpam-5208	32	7	has	have	AUX
ejpam-5208	32	8	been	be	AUX
ejpam-5208	32	9	studied	study	VERB
ejpam-5208	32	10	by	by	ADP
ejpam-5208	32	11	kadham	kadham	PROPN
ejpam-5208	32	12	and	and	CCONJ
ejpam-5208	32	13	hassan	hassan	PROPN
ejpam-5208	32	14	in	in	ADP
ejpam-5208	32	15	[	[	X
ejpam-5208	32	16	2	2	NUM
ejpam-5208	32	17	]	]	PUNCT
ejpam-5208	32	18	namely	namely	ADV
ejpam-5208	32	19	,	,	PUNCT
ejpam-5208	32	20	the	the	DET
ejpam-5208	32	21	λ	λ	NOUN
ejpam-5208	32	22	-	-	ADJ
ejpam-5208	32	23	continuous	continuous	ADJ
ejpam-5208	32	24	function	function	NOUN
ejpam-5208	32	25	.	.	PUNCT
ejpam-5208	33	1	furthermore	furthermore	ADV
ejpam-5208	33	2	,	,	PUNCT
ejpam-5208	33	3	a	a	DET
ejpam-5208	33	4	generalization	generalization	NOUN
ejpam-5208	33	5	of	of	ADP
ejpam-5208	33	6	λ	λ	NOUN
ejpam-5208	33	7	-	-	ADJ
ejpam-5208	33	8	continuous	continuous	ADJ
ejpam-5208	33	9	functions	function	NOUN
ejpam-5208	33	10	in	in	ADP
ejpam-5208	33	11	bitopological	bitopological	ADJ
ejpam-5208	33	12	spaces	space	NOUN
ejpam-5208	33	13	called	call	VERB
ejpam-5208	33	14	weakly	weakly	ADJ
ejpam-5208	33	15	λ	λ	ADJ
ejpam-5208	33	16	-	-	ADJ
ejpam-5208	33	17	continuous	continuous	ADJ
ejpam-5208	33	18	functions	function	NOUN
ejpam-5208	33	19	,	,	PUNCT
ejpam-5208	33	20	has	have	AUX
ejpam-5208	33	21	been	be	AUX
ejpam-5208	33	22	investigated	investigate	VERB
ejpam-5208	33	23	by	by	ADP
ejpam-5208	33	24	moosa	moosa	PROPN
ejpam-5208	33	25	meera	meera	PROPN
ejpam-5208	33	26	,	,	PUNCT
ejpam-5208	33	27	et	et	PROPN
ejpam-5208	33	28	.	.	PUNCT
ejpam-5208	34	1	al	al	PROPN
ejpam-5208	34	2	in	in	ADP
ejpam-5208	34	3	[	[	X
ejpam-5208	34	4	5	5	NUM
ejpam-5208	34	5	]	]	PUNCT
ejpam-5208	34	6	.	.	PUNCT
ejpam-5208	35	1	they	they	PRON
ejpam-5208	35	2	studied	study	VERB
ejpam-5208	35	3	several	several	ADJ
ejpam-5208	35	4	properties	property	NOUN
ejpam-5208	35	5	of	of	ADP
ejpam-5208	35	6	weakly	weakly	ADJ
ejpam-5208	35	7	λ	λ	ADJ
ejpam-5208	35	8	-	-	ADJ
ejpam-5208	35	9	continuous	continuous	ADJ
ejpam-5208	35	10	functions	function	NOUN
ejpam-5208	35	11	and	and	CCONJ
ejpam-5208	35	12	obtained	obtain	VERB
ejpam-5208	35	13	several	several	ADJ
ejpam-5208	35	14	characterizations	characterization	NOUN
ejpam-5208	35	15	.	.	PUNCT
ejpam-5208	36	1	in	in	ADP
ejpam-5208	36	2	2021	2021	NUM
ejpam-5208	36	3	,	,	PUNCT
ejpam-5208	36	4	sivanthi	sivanthi	ADV
ejpam-5208	36	5	and	and	CCONJ
ejpam-5208	36	6	leevathi	leevathi	ADJ
ejpam-5208	36	7	in	in	ADP
ejpam-5208	36	8	[	[	X
ejpam-5208	36	9	8	8	NUM
ejpam-5208	36	10	]	]	PUNCT
ejpam-5208	36	11	introduced	introduce	VERB
ejpam-5208	36	12	rg	rg	NOUN
ejpam-5208	36	13	-	-	PUNCT
ejpam-5208	36	14	continuous	continuous	ADJ
ejpam-5208	36	15	functions	function	NOUN
ejpam-5208	36	16	and	and	CCONJ
ejpam-5208	36	17	rg	rg	NOUN
ejpam-5208	36	18	-	-	PUNCT
ejpam-5208	36	19	irresolute	irresolute	ADJ
ejpam-5208	36	20	functions	function	NOUN
ejpam-5208	36	21	using	use	VERB
ejpam-5208	36	22	rg	rg	NOUN
ejpam-5208	36	23	-	-	PUNCT
ejpam-5208	36	24	closed	close	VERB
ejpam-5208	36	25	sets	set	NOUN
ejpam-5208	36	26	and	and	CCONJ
ejpam-5208	36	27	characterized	characterize	VERB
ejpam-5208	36	28	some	some	PRON
ejpam-5208	36	29	of	of	ADP
ejpam-5208	36	30	their	their	PRON
ejpam-5208	36	31	properties	property	NOUN
ejpam-5208	36	32	.	.	PUNCT
ejpam-5208	37	1	recently	recently	ADV
ejpam-5208	37	2	,	,	PUNCT
ejpam-5208	37	3	atewi	atewi	VERB
ejpam-5208	37	4	et.al	et.al	VERB
ejpam-5208	37	5	in	in	ADP
ejpam-5208	37	6	[	[	X
ejpam-5208	37	7	1	1	NUM
ejpam-5208	37	8	]	]	PUNCT
ejpam-5208	37	9	introduced	introduce	VERB
ejpam-5208	37	10	the	the	DET
ejpam-5208	37	11	concepts	concept	NOUN
ejpam-5208	37	12	of	of	ADP
ejpam-5208	37	13	ω	ω	ADJ
ejpam-5208	37	14	-	-	ADJ
ejpam-5208	37	15	continuous	continuous	ADJ
ejpam-5208	37	16	functions	function	NOUN
ejpam-5208	37	17	in	in	ADP
ejpam-5208	37	18	bitopological	bitopological	ADJ
ejpam-5208	37	19	spaces	space	NOUN
ejpam-5208	37	20	and	and	CCONJ
ejpam-5208	37	21	further	far	ADV
ejpam-5208	37	22	characterized	characterize	VERB
ejpam-5208	37	23	these	these	DET
ejpam-5208	37	24	concepts	concept	NOUN
ejpam-5208	37	25	.	.	PUNCT
ejpam-5208	38	1	with	with	ADP
ejpam-5208	38	2	all	all	DET
ejpam-5208	38	3	these	these	DET
ejpam-5208	38	4	concepts	concept	NOUN
ejpam-5208	38	5	in	in	ADP
ejpam-5208	38	6	mind	mind	NOUN
ejpam-5208	38	7	,	,	PUNCT
ejpam-5208	38	8	the	the	DET
ejpam-5208	38	9	author	author	NOUN
ejpam-5208	38	10	is	be	AUX
ejpam-5208	38	11	motivated	motivate	VERB
ejpam-5208	38	12	to	to	PART
ejpam-5208	38	13	define	define	VERB
ejpam-5208	38	14	and	and	CCONJ
ejpam-5208	38	15	introduce	introduce	VERB
ejpam-5208	38	16	(	(	PUNCT
ejpam-5208	38	17	i	i	NOUN
ejpam-5208	38	18	,	,	PUNCT
ejpam-5208	38	19	j)-ψgs	j)-ψgs	ADV
ejpam-5208	38	20	-	-	PUNCT
ejpam-5208	38	21	open	open	ADJ
ejpam-5208	39	1	and	and	CCONJ
ejpam-5208	39	2	(	(	PUNCT
ejpam-5208	39	3	i	i	NOUN
ejpam-5208	39	4	,	,	PUNCT
ejpam-5208	39	5	j)-ψgs	j)-ψgs	ADV
ejpam-5208	39	6	-	-	PUNCT
ejpam-5208	39	7	closed	close	VERB
ejpam-5208	39	8	functions	function	NOUN
ejpam-5208	39	9	,	,	PUNCT
ejpam-5208	39	10	(	(	PUNCT
ejpam-5208	39	11	i	i	INTJ
ejpam-5208	39	12	,	,	PUNCT
ejpam-5208	39	13	j)-ψgs	j)-ψgs	ADV
ejpam-5208	39	14	-	-	PUNCT
ejpam-5208	39	15	continuous	continuous	ADJ
ejpam-5208	39	16	functions	function	NOUN
ejpam-5208	39	17	,	,	PUNCT
ejpam-5208	39	18	and	and	CCONJ
ejpam-5208	39	19	(	(	PUNCT
ejpam-5208	39	20	i	i	NOUN
ejpam-5208	39	21	,	,	PUNCT
ejpam-5208	39	22	j)ψgs	j)ψgs	PROPN
ejpam-5208	39	23	-	-	PUNCT
ejpam-5208	39	24	irresolute	irresolute	ADJ
ejpam-5208	39	25	functions	function	NOUN
ejpam-5208	39	26	using	use	VERB
ejpam-5208	39	27	(	(	PUNCT
ejpam-5208	39	28	i	i	INTJ
ejpam-5208	39	29	,	,	PUNCT
ejpam-5208	39	30	j)-ψgs	j)-ψgs	ADV
ejpam-5208	39	31	-	-	PUNCT
ejpam-5208	39	32	closed	closed	ADJ
ejpam-5208	39	33	sets	set	NOUN
ejpam-5208	39	34	in	in	ADP
ejpam-5208	39	35	bitopological	bitopological	ADJ
ejpam-5208	39	36	spaces	space	NOUN
ejpam-5208	39	37	,	,	PUNCT
ejpam-5208	39	38	and	and	CCONJ
ejpam-5208	39	39	intends	intend	VERB
ejpam-5208	39	40	to	to	PART
ejpam-5208	39	41	investigate	investigate	VERB
ejpam-5208	39	42	its	its	PRON
ejpam-5208	39	43	properties	property	NOUN
ejpam-5208	39	44	and	and	CCONJ
ejpam-5208	39	45	characterizations	characterization	NOUN
ejpam-5208	39	46	.	.	PUNCT
ejpam-5208	40	1	the	the	DET
ejpam-5208	40	2	findings	finding	NOUN
ejpam-5208	40	3	of	of	ADP
ejpam-5208	40	4	this	this	DET
ejpam-5208	40	5	study	study	NOUN
ejpam-5208	40	6	could	could	AUX
ejpam-5208	40	7	serve	serve	VERB
ejpam-5208	40	8	as	as	ADP
ejpam-5208	40	9	a	a	DET
ejpam-5208	40	10	resource	resource	NOUN
ejpam-5208	40	11	for	for	ADP
ejpam-5208	40	12	future	future	ADJ
ejpam-5208	40	13	research	research	NOUN
ejpam-5208	40	14	and	and	CCONJ
ejpam-5208	40	15	possible	possible	ADJ
ejpam-5208	40	16	applications	application	NOUN
ejpam-5208	40	17	.	.	PUNCT
ejpam-5208	41	1	this	this	PRON
ejpam-5208	41	2	may	may	AUX
ejpam-5208	41	3	encourage	encourage	VERB
ejpam-5208	41	4	other	other	ADJ
ejpam-5208	41	5	mathematics	mathematics	NOUN
ejpam-5208	41	6	enthusiasts	enthusiast	NOUN
ejpam-5208	41	7	to	to	PART
ejpam-5208	41	8	discover	discover	VERB
ejpam-5208	41	9	more	more	ADJ
ejpam-5208	41	10	results	result	NOUN
ejpam-5208	41	11	and	and	CCONJ
ejpam-5208	41	12	establish	establish	VERB
ejpam-5208	41	13	new	new	ADJ
ejpam-5208	41	14	research	research	NOUN
ejpam-5208	41	15	directions	direction	NOUN
ejpam-5208	41	16	for	for	ADP
ejpam-5208	41	17	further	further	ADJ
ejpam-5208	41	18	study	study	NOUN
ejpam-5208	41	19	.	.	PUNCT
ejpam-5208	42	1	2	2	X
ejpam-5208	42	2	.	.	NUM
ejpam-5208	42	3	preliminaries	preliminary	NOUN
ejpam-5208	42	4	a	a	DET
ejpam-5208	42	5	collection	collection	NOUN
ejpam-5208	42	6	τ	τ	PROPN
ejpam-5208	42	7	of	of	ADP
ejpam-5208	42	8	subsets	subset	NOUN
ejpam-5208	42	9	of	of	ADP
ejpam-5208	42	10	a	a	DET
ejpam-5208	42	11	nonempty	nonempty	ADV
ejpam-5208	42	12	set	set	VERB
ejpam-5208	42	13	x	x	PUNCT
ejpam-5208	42	14	is	be	AUX
ejpam-5208	42	15	a	a	DET
ejpam-5208	42	16	topology	topology	NOUN
ejpam-5208	42	17	on	on	ADP
ejpam-5208	42	18	x	x	SYM
ejpam-5208	42	19	if	if	SCONJ
ejpam-5208	42	20	it	it	PRON
ejpam-5208	42	21	satisfies	satisfy	VERB
ejpam-5208	42	22	the	the	DET
ejpam-5208	42	23	conditions	condition	NOUN
ejpam-5208	42	24	:	:	PUNCT
ejpam-5208	42	25	(	(	PUNCT
ejpam-5208	42	26	i	i	NOUN
ejpam-5208	42	27	)	)	PUNCT
ejpam-5208	42	28	∅	∅	NOUN
ejpam-5208	42	29	,	,	PUNCT
ejpam-5208	42	30	x	x	SYM
ejpam-5208	42	31	∈	∈	PROPN
ejpam-5208	42	32	τ	τ	X
ejpam-5208	42	33	,	,	PUNCT
ejpam-5208	42	34	(	(	PUNCT
ejpam-5208	42	35	ii	ii	NOUN
ejpam-5208	42	36	)	)	PUNCT
ejpam-5208	42	37	{	{	PUNCT
ejpam-5208	42	38	mω	mω	NOUN
ejpam-5208	42	39	:	:	PUNCT
ejpam-5208	42	40	ω	ω	NUM
ejpam-5208	42	41	∈	∈	PROPN
ejpam-5208	42	42	ω	ω	PROPN
ejpam-5208	42	43	}	}	PUNCT
ejpam-5208	42	44	⊆	⊆	NUM
ejpam-5208	42	45	τ	τ	PROPN
ejpam-5208	42	46	implies	imply	VERB
ejpam-5208	42	47	∪ω∈ωmω	∪ω∈ωmω	PROPN
ejpam-5208	42	48	∈	∈	PROPN
ejpam-5208	42	49	τ	τ	X
ejpam-5208	42	50	,	,	PUNCT
ejpam-5208	42	51	and	and	CCONJ
ejpam-5208	42	52	(	(	PUNCT
ejpam-5208	42	53	iii	iii	X
ejpam-5208	42	54	)	)	PUNCT
ejpam-5208	42	55	a	a	PRON
ejpam-5208	42	56	,	,	PUNCT
ejpam-5208	42	57	b	b	X
ejpam-5208	42	58	∈	∈	PROPN
ejpam-5208	42	59	τ	τ	X
ejpam-5208	42	60	implies	imply	VERB
ejpam-5208	42	61	a	a	DET
ejpam-5208	42	62	∩	∩	ADJ
ejpam-5208	42	63	b	b	X
ejpam-5208	42	64	∈	∈	PROPN
ejpam-5208	42	65	τ	τ	X
ejpam-5208	42	66	.	.	PUNCT
ejpam-5208	43	1	if	if	SCONJ
ejpam-5208	43	2	τ	τ	PROPN
ejpam-5208	43	3	is	be	AUX
ejpam-5208	43	4	a	a	DET
ejpam-5208	43	5	topology	topology	NOUN
ejpam-5208	43	6	on	on	ADP
ejpam-5208	43	7	x	x	NOUN
ejpam-5208	43	8	,	,	PUNCT
ejpam-5208	43	9	then	then	ADV
ejpam-5208	43	10	(	(	PUNCT
ejpam-5208	43	11	x	x	X
ejpam-5208	43	12	,	,	PUNCT
ejpam-5208	43	13	τ	τ	X
ejpam-5208	43	14	)	)	PUNCT
ejpam-5208	43	15	is	be	AUX
ejpam-5208	43	16	called	call	VERB
ejpam-5208	43	17	a	a	DET
ejpam-5208	43	18	topological	topological	ADJ
ejpam-5208	43	19	space	space	NOUN
ejpam-5208	43	20	,	,	PUNCT
ejpam-5208	43	21	and	and	CCONJ
ejpam-5208	43	22	the	the	DET
ejpam-5208	43	23	elements	element	NOUN
ejpam-5208	43	24	of	of	ADP
ejpam-5208	43	25	τ	τ	PROPN
ejpam-5208	43	26	are	be	AUX
ejpam-5208	43	27	called	call	VERB
ejpam-5208	43	28	τ	τ	X
ejpam-5208	43	29	-open	-open	PROPN
ejpam-5208	43	30	(	(	PUNCT
ejpam-5208	43	31	or	or	CCONJ
ejpam-5208	43	32	simply	simply	ADV
ejpam-5208	43	33	open	open	ADJ
ejpam-5208	43	34	)	)	PUNCT
ejpam-5208	43	35	sets	set	NOUN
ejpam-5208	43	36	.	.	PUNCT
ejpam-5208	44	1	a	a	DET
ejpam-5208	44	2	subset	subset	NOUN
ejpam-5208	44	3	f	f	NOUN
ejpam-5208	44	4	of	of	ADP
ejpam-5208	44	5	x	x	PROPN
ejpam-5208	44	6	is	be	AUX
ejpam-5208	44	7	said	say	VERB
ejpam-5208	44	8	to	to	PART
ejpam-5208	44	9	be	be	AUX
ejpam-5208	44	10	τ	τ	X
ejpam-5208	44	11	-closed	-close	VERB
ejpam-5208	44	12	(	(	PUNCT
ejpam-5208	44	13	or	or	CCONJ
ejpam-5208	44	14	simply	simply	ADV
ejpam-5208	44	15	closed	closed	ADJ
ejpam-5208	44	16	)	)	PUNCT
ejpam-5208	44	17	if	if	SCONJ
ejpam-5208	44	18	its	its	PRON
ejpam-5208	44	19	complement	complement	NOUN
ejpam-5208	44	20	x∖f	x∖f	PROPN
ejpam-5208	44	21	is	be	AUX
ejpam-5208	44	22	open	open	ADJ
ejpam-5208	44	23	.	.	PUNCT
ejpam-5208	45	1	the	the	DET
ejpam-5208	45	2	interior	interior	NOUN
ejpam-5208	45	3	of	of	ADP
ejpam-5208	45	4	a	a	PRON
ejpam-5208	45	5	,	,	PUNCT
ejpam-5208	45	6	denoted	denote	VERB
ejpam-5208	45	7	by	by	ADP
ejpam-5208	45	8	int(a	int(a	PROPN
ejpam-5208	45	9	)	)	PUNCT
ejpam-5208	45	10	,	,	PUNCT
ejpam-5208	45	11	is	be	AUX
ejpam-5208	45	12	the	the	DET
ejpam-5208	45	13	union	union	NOUN
ejpam-5208	45	14	of	of	ADP
ejpam-5208	45	15	all	all	DET
ejpam-5208	45	16	open	open	ADJ
ejpam-5208	45	17	sets	set	NOUN
ejpam-5208	45	18	contained	contain	VERB
ejpam-5208	45	19	in	in	ADP
ejpam-5208	45	20	a.	a.	NOUN
ejpam-5208	45	21	that	that	PRON
ejpam-5208	45	22	is	be	AUX
ejpam-5208	45	23	,	,	PUNCT
ejpam-5208	45	24	int(a	int(a	PROPN
ejpam-5208	45	25	)	)	PUNCT
ejpam-5208	45	26	=	=	SYM
ejpam-5208	45	27	⋃	⋃	NOUN
ejpam-5208	45	28	{	{	PUNCT
ejpam-5208	45	29	o	o	NOUN
ejpam-5208	45	30	∈	∈	PROPN
ejpam-5208	45	31	τ	τ	X
ejpam-5208	45	32	:	:	PUNCT
ejpam-5208	45	33	o	o	X
ejpam-5208	45	34	⊆	⊆	NUM
ejpam-5208	45	35	a	a	PRON
ejpam-5208	45	36	}	}	PUNCT
ejpam-5208	45	37	.	.	PUNCT
ejpam-5208	46	1	the	the	DET
ejpam-5208	46	2	closure	closure	NOUN
ejpam-5208	46	3	of	of	ADP
ejpam-5208	46	4	a	a	PRON
ejpam-5208	46	5	,	,	PUNCT
ejpam-5208	46	6	denoted	denote	VERB
ejpam-5208	46	7	by	by	ADP
ejpam-5208	46	8	cl(a	cl(a	NOUN
ejpam-5208	46	9	)	)	PUNCT
ejpam-5208	46	10	,	,	PUNCT
ejpam-5208	46	11	is	be	AUX
ejpam-5208	46	12	the	the	DET
ejpam-5208	46	13	intersection	intersection	NOUN
ejpam-5208	46	14	of	of	ADP
ejpam-5208	46	15	all	all	DET
ejpam-5208	46	16	closed	closed	ADJ
ejpam-5208	46	17	sets	set	NOUN
ejpam-5208	46	18	containing	contain	VERB
ejpam-5208	46	19	a.	a.	NOUN
ejpam-5208	46	20	that	that	PRON
ejpam-5208	46	21	is	be	AUX
ejpam-5208	46	22	,	,	PUNCT
ejpam-5208	46	23	cl(a	cl(a	X
ejpam-5208	46	24	)	)	PUNCT
ejpam-5208	46	25	=	=	SYM
ejpam-5208	46	26	⋂	⋂	PROPN
ejpam-5208	46	27	{	{	PUNCT
ejpam-5208	46	28	f	f	NOUN
ejpam-5208	46	29	⊆	⊆	NUM
ejpam-5208	46	30	x	x	X
ejpam-5208	46	31	:	:	PUNCT
ejpam-5208	46	32	f	f	PROPN
ejpam-5208	46	33	is	be	AUX
ejpam-5208	46	34	closed	closed	ADJ
ejpam-5208	46	35	and	and	CCONJ
ejpam-5208	46	36	a	a	DET
ejpam-5208	46	37	⊆	⊆	NUM
ejpam-5208	46	38	f	f	NOUN
ejpam-5208	46	39	}	}	PUNCT
ejpam-5208	46	40	.	.	PUNCT
ejpam-5208	47	1	a	a	DET
ejpam-5208	47	2	set	set	NOUN
ejpam-5208	47	3	x	x	PUNCT
ejpam-5208	47	4	endowed	endow	VERB
ejpam-5208	47	5	with	with	ADP
ejpam-5208	47	6	two	two	NUM
ejpam-5208	47	7	topologies	topology	NOUN
ejpam-5208	47	8	,	,	PUNCT
ejpam-5208	47	9	τ1	τ1	NOUN
ejpam-5208	47	10	and	and	CCONJ
ejpam-5208	47	11	τ2	τ2	NOUN
ejpam-5208	47	12	,	,	PUNCT
ejpam-5208	47	13	is	be	AUX
ejpam-5208	47	14	called	call	VERB
ejpam-5208	47	15	a	a	DET
ejpam-5208	47	16	bitopological	bitopological	ADJ
ejpam-5208	47	17	space	space	NOUN
ejpam-5208	47	18	(	(	PUNCT
ejpam-5208	47	19	abbreviated	abbreviate	VERB
ejpam-5208	47	20	as	as	ADP
ejpam-5208	47	21	bts	bt	NOUN
ejpam-5208	47	22	)	)	PUNCT
ejpam-5208	47	23	and	and	CCONJ
ejpam-5208	47	24	denoted	denote	VERB
ejpam-5208	47	25	as	as	ADP
ejpam-5208	47	26	(	(	PUNCT
ejpam-5208	47	27	x	x	NOUN
ejpam-5208	47	28	,	,	PUNCT
ejpam-5208	47	29	τ1	τ1	NOUN
ejpam-5208	47	30	,	,	PUNCT
ejpam-5208	47	31	τ2	τ2	NOUN
ejpam-5208	47	32	)	)	PUNCT
ejpam-5208	47	33	.	.	PUNCT
ejpam-5208	48	1	an	an	DET
ejpam-5208	48	2	open	open	ADJ
ejpam-5208	48	3	set	set	NOUN
ejpam-5208	48	4	in	in	ADP
ejpam-5208	48	5	a	a	DET
ejpam-5208	48	6	bts	bt	NOUN
ejpam-5208	48	7	is	be	AUX
ejpam-5208	48	8	denoted	denote	VERB
ejpam-5208	48	9	by	by	ADP
ejpam-5208	48	10	τi	τi	ADV
ejpam-5208	48	11	-	-	PUNCT
ejpam-5208	48	12	open	open	ADJ
ejpam-5208	48	13	,	,	PUNCT
ejpam-5208	48	14	l.	l.	PROPN
ejpam-5208	48	15	m.	m.	PROPN
ejpam-5208	48	16	tutanes	tutane	VERB
ejpam-5208	48	17	/	/	SYM
ejpam-5208	48	18	eur	eur	PROPN
ejpam-5208	48	19	.	.	PUNCT
ejpam-5208	49	1	j.	j.	PROPN
ejpam-5208	49	2	pure	pure	PROPN
ejpam-5208	49	3	appl	appl	PROPN
ejpam-5208	49	4	.	.	PROPN
ejpam-5208	49	5	math	math	PROPN
ejpam-5208	49	6	,	,	PUNCT
ejpam-5208	49	7	17	17	NUM
ejpam-5208	49	8	(	(	PUNCT
ejpam-5208	49	9	3	3	NUM
ejpam-5208	49	10	)	)	PUNCT
ejpam-5208	49	11	(	(	PUNCT
ejpam-5208	49	12	2024	2024	NUM
ejpam-5208	49	13	)	)	PUNCT
ejpam-5208	49	14	,	,	PUNCT
ejpam-5208	49	15	2173	2173	NUM
ejpam-5208	49	16	-	-	SYM
ejpam-5208	49	17	2181	2181	NUM
ejpam-5208	49	18	2175	2175	NUM
ejpam-5208	49	19	where	where	SCONJ
ejpam-5208	49	20	i	i	PRON
ejpam-5208	49	21	∈	∈	PROPN
ejpam-5208	49	22	{	{	PUNCT
ejpam-5208	49	23	1	1	NUM
ejpam-5208	49	24	,	,	PUNCT
ejpam-5208	49	25	2	2	NUM
ejpam-5208	49	26	}	}	PUNCT
ejpam-5208	49	27	.	.	PUNCT
ejpam-5208	50	1	the	the	DET
ejpam-5208	50	2	interior	interior	ADJ
ejpam-5208	50	3	and	and	CCONJ
ejpam-5208	50	4	closure	closure	NOUN
ejpam-5208	50	5	of	of	ADP
ejpam-5208	50	6	a	a	DET
ejpam-5208	50	7	subset	subset	NOUN
ejpam-5208	50	8	a	a	PRON
ejpam-5208	50	9	of	of	ADP
ejpam-5208	50	10	x	x	PRON
ejpam-5208	50	11	in	in	ADP
ejpam-5208	50	12	a	a	DET
ejpam-5208	50	13	bts	bt	NOUN
ejpam-5208	50	14	are	be	AUX
ejpam-5208	50	15	written	write	VERB
ejpam-5208	50	16	as	as	ADP
ejpam-5208	50	17	inti(a	inti(a	PROPN
ejpam-5208	50	18	)	)	PUNCT
ejpam-5208	50	19	and	and	CCONJ
ejpam-5208	50	20	cli(a	cli(a	PROPN
ejpam-5208	50	21	)	)	PUNCT
ejpam-5208	50	22	,	,	PUNCT
ejpam-5208	50	23	respectively	respectively	ADV
ejpam-5208	50	24	.	.	PUNCT
ejpam-5208	51	1	the	the	DET
ejpam-5208	51	2	following	follow	VERB
ejpam-5208	51	3	definitions	definition	NOUN
ejpam-5208	51	4	in	in	ADP
ejpam-5208	51	5	bts	bt	NOUN
ejpam-5208	51	6	,	,	PUNCT
ejpam-5208	51	7	as	as	SCONJ
ejpam-5208	51	8	introduced	introduce	VERB
ejpam-5208	51	9	in	in	ADP
ejpam-5208	51	10	[	[	X
ejpam-5208	51	11	11	11	NUM
ejpam-5208	51	12	]	]	PUNCT
ejpam-5208	51	13	,	,	PUNCT
ejpam-5208	51	14	are	be	AUX
ejpam-5208	51	15	pertinent	pertinent	ADJ
ejpam-5208	51	16	to	to	ADP
ejpam-5208	51	17	this	this	DET
ejpam-5208	51	18	study	study	NOUN
ejpam-5208	51	19	.	.	PUNCT
ejpam-5208	52	1	definition	definition	NOUN
ejpam-5208	52	2	1	1	NUM
ejpam-5208	52	3	.	.	PUNCT
ejpam-5208	53	1	a	a	DET
ejpam-5208	53	2	subset	subset	NOUN
ejpam-5208	53	3	a	a	PRON
ejpam-5208	53	4	of	of	ADP
ejpam-5208	53	5	a	a	DET
ejpam-5208	53	6	bitopological	bitopological	ADJ
ejpam-5208	53	7	space	space	NOUN
ejpam-5208	53	8	(	(	PUNCT
ejpam-5208	53	9	x	x	NOUN
ejpam-5208	53	10	,	,	PUNCT
ejpam-5208	53	11	τ1	τ1	NOUN
ejpam-5208	53	12	,	,	PUNCT
ejpam-5208	53	13	τ2	τ2	NOUN
ejpam-5208	53	14	)	)	PUNCT
ejpam-5208	53	15	is	be	AUX
ejpam-5208	53	16	called	call	VERB
ejpam-5208	53	17	(	(	PUNCT
ejpam-5208	53	18	i	i	PROPN
ejpam-5208	53	19	,	,	PUNCT
ejpam-5208	53	20	j)-ψ	j)-ψ	PROPN
ejpam-5208	53	21	generalized	generalize	VERB
ejpam-5208	53	22	semi	semi	ADV
ejpam-5208	53	23	-	-	ADJ
ejpam-5208	53	24	closed	closed	ADJ
ejpam-5208	53	25	(	(	PUNCT
ejpam-5208	53	26	briefly	briefly	ADV
ejpam-5208	53	27	,	,	PUNCT
ejpam-5208	53	28	(	(	PUNCT
ejpam-5208	53	29	i	i	INTJ
ejpam-5208	53	30	,	,	PUNCT
ejpam-5208	53	31	j)-ψgs	j)-ψgs	ADV
ejpam-5208	53	32	-	-	PUNCT
ejpam-5208	53	33	closed	closed	ADJ
ejpam-5208	53	34	)	)	PUNCT
ejpam-5208	53	35	set	set	VERB
ejpam-5208	53	36	if	if	SCONJ
ejpam-5208	53	37	(	(	PUNCT
ejpam-5208	53	38	i	i	NOUN
ejpam-5208	53	39	,	,	PUNCT
ejpam-5208	53	40	j)-ψcl(a	j)-ψcl(a	PROPN
ejpam-5208	53	41	)	)	PUNCT
ejpam-5208	53	42	⊆	⊆	NUM
ejpam-5208	53	43	u	u	NOUN
ejpam-5208	53	44	whenever	whenever	SCONJ
ejpam-5208	53	45	a	a	DET
ejpam-5208	53	46	⊆	⊆	NUM
ejpam-5208	53	47	u	u	NOUN
ejpam-5208	53	48	,	,	PUNCT
ejpam-5208	53	49	u	u	NOUN
ejpam-5208	53	50	is	be	AUX
ejpam-5208	53	51	(	(	PUNCT
ejpam-5208	53	52	i	i	PROPN
ejpam-5208	53	53	,	,	PUNCT
ejpam-5208	53	54	j)-semi	j)-semi	NOUN
ejpam-5208	53	55	-	-	PUNCT
ejpam-5208	53	56	open	open	ADJ
ejpam-5208	53	57	in	in	ADP
ejpam-5208	53	58	(	(	PUNCT
ejpam-5208	53	59	x	x	NOUN
ejpam-5208	53	60	,	,	PUNCT
ejpam-5208	53	61	τ1	τ1	NOUN
ejpam-5208	53	62	,	,	PUNCT
ejpam-5208	53	63	τ2	τ2	NOUN
ejpam-5208	53	64	)	)	PUNCT
ejpam-5208	53	65	,	,	PUNCT
ejpam-5208	53	66	i	i	PRON
ejpam-5208	53	67	,	,	PUNCT
ejpam-5208	53	68	j	j	PROPN
ejpam-5208	53	69	∈	∈	PROPN
ejpam-5208	53	70	{	{	PUNCT
ejpam-5208	53	71	1	1	NUM
ejpam-5208	53	72	,	,	PUNCT
ejpam-5208	53	73	2	2	NUM
ejpam-5208	53	74	}	}	PUNCT
ejpam-5208	53	75	and	and	CCONJ
ejpam-5208	53	76	i	i	PRON
ejpam-5208	53	77	̸=	̸=	PROPN
ejpam-5208	53	78	j.	j.	PROPN
ejpam-5208	53	79	definition	definition	NOUN
ejpam-5208	53	80	2	2	NUM
ejpam-5208	53	81	.	.	PUNCT
ejpam-5208	54	1	let	let	AUX
ejpam-5208	54	2	(	(	PUNCT
ejpam-5208	54	3	x	x	NOUN
ejpam-5208	54	4	,	,	PUNCT
ejpam-5208	54	5	τ1	τ1	NOUN
ejpam-5208	54	6	,	,	PUNCT
ejpam-5208	54	7	τ2	τ2	PROPN
ejpam-5208	54	8	)	)	PUNCT
ejpam-5208	54	9	be	be	VERB
ejpam-5208	54	10	a	a	DET
ejpam-5208	54	11	bitopological	bitopological	ADJ
ejpam-5208	54	12	space	space	NOUN
ejpam-5208	54	13	and	and	CCONJ
ejpam-5208	54	14	a	a	DET
ejpam-5208	54	15	⊆	⊆	NUM
ejpam-5208	54	16	x.	x.	NOUN
ejpam-5208	54	17	an	an	DET
ejpam-5208	54	18	element	element	NOUN
ejpam-5208	54	19	x	x	SYM
ejpam-5208	54	20	∈	∈	PROPN
ejpam-5208	54	21	a	a	PRON
ejpam-5208	54	22	is	be	AUX
ejpam-5208	54	23	called	call	VERB
ejpam-5208	54	24	(	(	PUNCT
ejpam-5208	54	25	i	i	PROPN
ejpam-5208	54	26	,	,	PUNCT
ejpam-5208	54	27	j)-ψgs	j)-ψgs	ADJ
ejpam-5208	54	28	-	-	ADJ
ejpam-5208	54	29	interior	interior	ADJ
ejpam-5208	54	30	point	point	NOUN
ejpam-5208	54	31	of	of	ADP
ejpam-5208	54	32	a	a	PRON
ejpam-5208	54	33	if	if	SCONJ
ejpam-5208	54	34	there	there	PRON
ejpam-5208	54	35	exists	exist	VERB
ejpam-5208	54	36	an	an	DET
ejpam-5208	54	37	(	(	PUNCT
ejpam-5208	54	38	i	i	NOUN
ejpam-5208	54	39	,	,	PUNCT
ejpam-5208	54	40	j)-ψgs	j)-ψgs	ADV
ejpam-5208	54	41	-	-	ADJ
ejpam-5208	54	42	open	open	ADJ
ejpam-5208	54	43	set	set	ADJ
ejpam-5208	54	44	o	o	NOUN
ejpam-5208	55	1	such	such	ADJ
ejpam-5208	55	2	that	that	SCONJ
ejpam-5208	55	3	x	x	SYM
ejpam-5208	55	4	∈	∈	NOUN
ejpam-5208	55	5	o	o	NOUN
ejpam-5208	55	6	⊆	⊆	NUM
ejpam-5208	55	7	a.	a.	NOUN
ejpam-5208	55	8	the	the	DET
ejpam-5208	55	9	set	set	NOUN
ejpam-5208	55	10	of	of	ADP
ejpam-5208	55	11	all	all	DET
ejpam-5208	55	12	(	(	PUNCT
ejpam-5208	55	13	i	i	NOUN
ejpam-5208	55	14	,	,	PUNCT
ejpam-5208	55	15	j)-ψgs	j)-ψgs	ADJ
ejpam-5208	55	16	-	-	ADJ
ejpam-5208	55	17	interior	interior	ADJ
ejpam-5208	55	18	points	point	NOUN
ejpam-5208	55	19	of	of	ADP
ejpam-5208	55	20	a	a	PRON
ejpam-5208	55	21	is	be	AUX
ejpam-5208	55	22	called	call	VERB
ejpam-5208	55	23	the	the	DET
ejpam-5208	55	24	(	(	PUNCT
ejpam-5208	55	25	i	i	PROPN
ejpam-5208	55	26	,	,	PUNCT
ejpam-5208	55	27	j)-ψgs	j)-ψgs	ADV
ejpam-5208	55	28	-	-	ADJ
ejpam-5208	55	29	interior	interior	ADJ
ejpam-5208	55	30	of	of	ADP
ejpam-5208	55	31	a	a	PRON
ejpam-5208	55	32	and	and	CCONJ
ejpam-5208	55	33	is	be	AUX
ejpam-5208	55	34	denoted	denote	VERB
ejpam-5208	55	35	by	by	ADP
ejpam-5208	55	36	(	(	PUNCT
ejpam-5208	55	37	i	i	INTJ
ejpam-5208	55	38	,	,	PUNCT
ejpam-5208	55	39	j)-ψgs	j)-ψgs	ADV
ejpam-5208	55	40	-	-	PUNCT
ejpam-5208	55	41	int(a	int(a	NOUN
ejpam-5208	55	42	)	)	PUNCT
ejpam-5208	56	1	.	.	PUNCT
ejpam-5208	57	1	definition	definition	NOUN
ejpam-5208	57	2	3	3	X
ejpam-5208	57	3	.	.	PUNCT
ejpam-5208	58	1	let	let	VERB
ejpam-5208	58	2	a	a	DET
ejpam-5208	58	3	⊆	⊆	NUM
ejpam-5208	58	4	x.	x.	NOUN
ejpam-5208	58	5	then	then	ADV
ejpam-5208	58	6	x	x	SYM
ejpam-5208	58	7	∈	∈	PROPN
ejpam-5208	58	8	x	x	X
ejpam-5208	58	9	is	be	AUX
ejpam-5208	58	10	(	(	PUNCT
ejpam-5208	58	11	i	i	NOUN
ejpam-5208	58	12	,	,	PUNCT
ejpam-5208	58	13	j)-ψgs	j)-ψgs	ADV
ejpam-5208	58	14	-	-	PUNCT
ejpam-5208	58	15	adherent	adherent	ADJ
ejpam-5208	58	16	to	to	ADP
ejpam-5208	58	17	a	a	DET
ejpam-5208	58	18	if	if	SCONJ
ejpam-5208	58	19	v	v	NOUN
ejpam-5208	58	20	∩a	∩a	PROPN
ejpam-5208	58	21	̸=	̸=	PROPN
ejpam-5208	58	22	∅	∅	NOUN
ejpam-5208	58	23	for	for	ADP
ejpam-5208	58	24	every	every	DET
ejpam-5208	58	25	(	(	PUNCT
ejpam-5208	58	26	i	i	NOUN
ejpam-5208	58	27	,	,	PUNCT
ejpam-5208	58	28	j)-ψgs	j)-ψgs	ADV
ejpam-5208	58	29	-	-	ADJ
ejpam-5208	58	30	open	open	ADJ
ejpam-5208	58	31	set	set	VERB
ejpam-5208	58	32	v	v	NOUN
ejpam-5208	58	33	containing	contain	VERB
ejpam-5208	58	34	x.	x.	NOUN
ejpam-5208	58	35	the	the	DET
ejpam-5208	58	36	set	set	NOUN
ejpam-5208	58	37	of	of	ADP
ejpam-5208	58	38	all	all	DET
ejpam-5208	58	39	(	(	PUNCT
ejpam-5208	58	40	i	i	NOUN
ejpam-5208	58	41	,	,	PUNCT
ejpam-5208	58	42	j)-ψgs	j)-ψgs	ADJ
ejpam-5208	58	43	-	-	PUNCT
ejpam-5208	58	44	adherent	adherent	ADJ
ejpam-5208	58	45	points	point	NOUN
ejpam-5208	58	46	of	of	ADP
ejpam-5208	58	47	a	a	PRON
ejpam-5208	58	48	is	be	AUX
ejpam-5208	58	49	called	call	VERB
ejpam-5208	58	50	the	the	DET
ejpam-5208	58	51	(	(	PUNCT
ejpam-5208	58	52	i	i	NOUN
ejpam-5208	58	53	,	,	PUNCT
ejpam-5208	58	54	j)-ψgs	j)-ψgs	ADV
ejpam-5208	58	55	-	-	PUNCT
ejpam-5208	58	56	closure	closure	NOUN
ejpam-5208	58	57	of	of	ADP
ejpam-5208	58	58	a	a	PRON
ejpam-5208	58	59	and	and	CCONJ
ejpam-5208	58	60	is	be	AUX
ejpam-5208	58	61	denoted	denote	VERB
ejpam-5208	58	62	by	by	ADP
ejpam-5208	58	63	(	(	PUNCT
ejpam-5208	58	64	i	i	INTJ
ejpam-5208	58	65	,	,	PUNCT
ejpam-5208	58	66	j)-ψgs	j)-ψgs	ADV
ejpam-5208	58	67	-	-	PUNCT
ejpam-5208	58	68	cl(a	cl(a	NUM
ejpam-5208	58	69	)	)	PUNCT
ejpam-5208	58	70	.	.	PUNCT
ejpam-5208	59	1	the	the	DET
ejpam-5208	59	2	following	follow	VERB
ejpam-5208	59	3	results	result	NOUN
ejpam-5208	59	4	from	from	ADP
ejpam-5208	59	5	[	[	X
ejpam-5208	59	6	11	11	NUM
ejpam-5208	59	7	]	]	PUNCT
ejpam-5208	59	8	are	be	AUX
ejpam-5208	59	9	crucial	crucial	ADJ
ejpam-5208	59	10	for	for	ADP
ejpam-5208	59	11	demonstrating	demonstrate	VERB
ejpam-5208	59	12	certain	certain	ADJ
ejpam-5208	59	13	findings	finding	NOUN
ejpam-5208	59	14	in	in	ADP
ejpam-5208	59	15	this	this	DET
ejpam-5208	59	16	study	study	NOUN
ejpam-5208	59	17	.	.	PUNCT
ejpam-5208	60	1	corollary	corollary	ADJ
ejpam-5208	60	2	1	1	NUM
ejpam-5208	60	3	.	.	PUNCT
ejpam-5208	61	1	let	let	AUX
ejpam-5208	61	2	(	(	PUNCT
ejpam-5208	61	3	y	y	NOUN
ejpam-5208	61	4	,	,	PUNCT
ejpam-5208	61	5	σi	σi	NOUN
ejpam-5208	61	6	)	)	PUNCT
ejpam-5208	61	7	be	be	VERB
ejpam-5208	61	8	a	a	DET
ejpam-5208	61	9	topological	topological	ADJ
ejpam-5208	61	10	space	space	NOUN
ejpam-5208	61	11	and	and	CCONJ
ejpam-5208	61	12	(	(	PUNCT
ejpam-5208	61	13	y	y	PROPN
ejpam-5208	61	14	,	,	PUNCT
ejpam-5208	61	15	σ1	σ1	PROPN
ejpam-5208	61	16	,	,	PUNCT
ejpam-5208	61	17	σ2	σ2	PROPN
ejpam-5208	61	18	)	)	PUNCT
ejpam-5208	61	19	be	be	AUX
ejpam-5208	61	20	a	a	DET
ejpam-5208	61	21	bitopological	bitopological	ADJ
ejpam-5208	61	22	space	space	NOUN
ejpam-5208	61	23	.	.	PUNCT
ejpam-5208	62	1	then	then	ADV
ejpam-5208	62	2	every	every	DET
ejpam-5208	62	3	σi	σi	NOUN
ejpam-5208	62	4	-	-	PUNCT
ejpam-5208	62	5	closed	closed	ADJ
ejpam-5208	62	6	set	set	NOUN
ejpam-5208	62	7	is	be	AUX
ejpam-5208	62	8	(	(	PUNCT
ejpam-5208	62	9	i	i	PROPN
ejpam-5208	62	10	,	,	PUNCT
ejpam-5208	62	11	j)-ψgs	j)-ψgs	ADV
ejpam-5208	62	12	-	-	PUNCT
ejpam-5208	62	13	closed	closed	ADJ
ejpam-5208	62	14	set	set	NOUN
ejpam-5208	62	15	.	.	PUNCT
ejpam-5208	63	1	remark	remark	PROPN
ejpam-5208	63	2	1	1	NUM
ejpam-5208	63	3	.	.	PUNCT
ejpam-5208	64	1	let	let	AUX
ejpam-5208	64	2	(	(	PUNCT
ejpam-5208	64	3	x	x	NOUN
ejpam-5208	64	4	,	,	PUNCT
ejpam-5208	64	5	τ1	τ1	NOUN
ejpam-5208	64	6	,	,	PUNCT
ejpam-5208	64	7	τ2	τ2	PROPN
ejpam-5208	64	8	)	)	PUNCT
ejpam-5208	64	9	be	be	VERB
ejpam-5208	64	10	a	a	DET
ejpam-5208	64	11	bitopological	bitopological	ADJ
ejpam-5208	64	12	space	space	NOUN
ejpam-5208	64	13	and	and	CCONJ
ejpam-5208	64	14	a	a	PRON
ejpam-5208	64	15	,	,	PUNCT
ejpam-5208	64	16	b	b	PROPN
ejpam-5208	64	17	⊆	⊆	NUM
ejpam-5208	64	18	x.	x.	NOUN
ejpam-5208	64	19	then	then	ADV
ejpam-5208	64	20	the	the	DET
ejpam-5208	64	21	following	follow	VERB
ejpam-5208	64	22	hold	hold	NOUN
ejpam-5208	64	23	:	:	PUNCT
ejpam-5208	64	24	(	(	PUNCT
ejpam-5208	64	25	i	i	NOUN
ejpam-5208	64	26	)	)	PUNCT
ejpam-5208	64	27	(	(	PUNCT
ejpam-5208	64	28	i	i	NOUN
ejpam-5208	64	29	,	,	PUNCT
ejpam-5208	64	30	j)-ψgs	j)-ψgs	ADV
ejpam-5208	64	31	-	-	PUNCT
ejpam-5208	64	32	int(a	int(a	NOUN
ejpam-5208	64	33	)	)	PUNCT
ejpam-5208	64	34	⊆	⊆	PROPN
ejpam-5208	64	35	a	a	PRON
ejpam-5208	64	36	;	;	PUNCT
ejpam-5208	64	37	(	(	PUNCT
ejpam-5208	64	38	ii	ii	NOUN
ejpam-5208	64	39	)	)	PUNCT
ejpam-5208	64	40	(	(	PUNCT
ejpam-5208	64	41	i	i	NOUN
ejpam-5208	64	42	,	,	PUNCT
ejpam-5208	64	43	j)-ψgs	j)-ψgs	ADV
ejpam-5208	64	44	-	-	PUNCT
ejpam-5208	64	45	int(a	int(a	NOUN
ejpam-5208	64	46	)	)	PUNCT
ejpam-5208	64	47	is	be	AUX
ejpam-5208	64	48	(	(	PUNCT
ejpam-5208	64	49	i	i	NOUN
ejpam-5208	64	50	,	,	PUNCT
ejpam-5208	64	51	j)-ψgs	j)-ψgs	ADV
ejpam-5208	64	52	-	-	PUNCT
ejpam-5208	64	53	open	open	ADJ
ejpam-5208	64	54	set	set	NOUN
ejpam-5208	64	55	;	;	PUNCT
ejpam-5208	64	56	and	and	CCONJ
ejpam-5208	64	57	(	(	PUNCT
ejpam-5208	64	58	iii	iii	X
ejpam-5208	64	59	)	)	PUNCT
ejpam-5208	64	60	if	if	SCONJ
ejpam-5208	64	61	b	b	PROPN
ejpam-5208	64	62	⊆	⊆	SYM
ejpam-5208	64	63	a	a	DET
ejpam-5208	64	64	such	such	ADJ
ejpam-5208	64	65	that	that	DET
ejpam-5208	64	66	b	b	NOUN
ejpam-5208	64	67	is	be	AUX
ejpam-5208	64	68	(	(	PUNCT
ejpam-5208	64	69	i	i	NOUN
ejpam-5208	64	70	,	,	PUNCT
ejpam-5208	64	71	j)-ψgs	j)-ψgs	ADV
ejpam-5208	64	72	-	-	PUNCT
ejpam-5208	64	73	open	open	ADJ
ejpam-5208	64	74	set	set	NOUN
ejpam-5208	64	75	,	,	PUNCT
ejpam-5208	64	76	then	then	ADV
ejpam-5208	64	77	b	b	PROPN
ejpam-5208	64	78	⊆	⊆	NUM
ejpam-5208	64	79	(	(	PUNCT
ejpam-5208	64	80	i	i	NOUN
ejpam-5208	64	81	,	,	PUNCT
ejpam-5208	64	82	j)-ψgs	j)-ψgs	ADV
ejpam-5208	64	83	-	-	PUNCT
ejpam-5208	64	84	int(a	int(a	NOUN
ejpam-5208	64	85	)	)	PUNCT
ejpam-5208	64	86	.	.	PUNCT
ejpam-5208	65	1	theorem	theorem	NOUN
ejpam-5208	65	2	1	1	X
ejpam-5208	65	3	.	.	PUNCT
ejpam-5208	66	1	let	let	AUX
ejpam-5208	66	2	(	(	PUNCT
ejpam-5208	66	3	x	x	NOUN
ejpam-5208	66	4	,	,	PUNCT
ejpam-5208	66	5	τ1	τ1	NOUN
ejpam-5208	66	6	,	,	PUNCT
ejpam-5208	66	7	τ2	τ2	PROPN
ejpam-5208	66	8	)	)	PUNCT
ejpam-5208	66	9	be	be	VERB
ejpam-5208	66	10	a	a	DET
ejpam-5208	66	11	bitopological	bitopological	ADJ
ejpam-5208	66	12	space	space	NOUN
ejpam-5208	66	13	and	and	CCONJ
ejpam-5208	66	14	a	a	DET
ejpam-5208	66	15	⊆	⊆	NUM
ejpam-5208	66	16	x.	x.	NOUN
ejpam-5208	66	17	a	a	DET
ejpam-5208	66	18	set	set	NOUN
ejpam-5208	66	19	a	a	PRON
ejpam-5208	66	20	is	be	AUX
ejpam-5208	66	21	(	(	PUNCT
ejpam-5208	66	22	i	i	NOUN
ejpam-5208	66	23	,	,	PUNCT
ejpam-5208	66	24	j)-ψgs	j)-ψgs	ADV
ejpam-5208	66	25	-	-	PUNCT
ejpam-5208	66	26	open	open	ADJ
ejpam-5208	66	27	set	set	NOUN
ejpam-5208	66	28	,	,	PUNCT
ejpam-5208	66	29	if	if	SCONJ
ejpam-5208	66	30	and	and	CCONJ
ejpam-5208	66	31	only	only	ADV
ejpam-5208	66	32	if	if	SCONJ
ejpam-5208	66	33	(	(	PUNCT
ejpam-5208	66	34	i	i	NOUN
ejpam-5208	66	35	,	,	PUNCT
ejpam-5208	66	36	j)-ψgs	j)-ψgs	ADV
ejpam-5208	66	37	-	-	PUNCT
ejpam-5208	66	38	int(a	int(a	NOUN
ejpam-5208	66	39	)	)	PUNCT
ejpam-5208	66	40	=	=	NOUN
ejpam-5208	66	41	a.	a.	NOUN
ejpam-5208	66	42	remark	remark	NOUN
ejpam-5208	66	43	2	2	NUM
ejpam-5208	66	44	.	.	PUNCT
ejpam-5208	67	1	let	let	AUX
ejpam-5208	67	2	(	(	PUNCT
ejpam-5208	67	3	x	x	NOUN
ejpam-5208	67	4	,	,	PUNCT
ejpam-5208	67	5	τ1	τ1	NOUN
ejpam-5208	67	6	,	,	PUNCT
ejpam-5208	67	7	τ2	τ2	PROPN
ejpam-5208	67	8	)	)	PUNCT
ejpam-5208	67	9	be	be	VERB
ejpam-5208	67	10	a	a	DET
ejpam-5208	67	11	bitopological	bitopological	ADJ
ejpam-5208	67	12	space	space	NOUN
ejpam-5208	67	13	and	and	CCONJ
ejpam-5208	67	14	a	a	PRON
ejpam-5208	67	15	,	,	PUNCT
ejpam-5208	67	16	b	b	PROPN
ejpam-5208	67	17	⊆	⊆	NUM
ejpam-5208	67	18	x.	x.	NOUN
ejpam-5208	67	19	then	then	ADV
ejpam-5208	67	20	the	the	DET
ejpam-5208	67	21	following	follow	VERB
ejpam-5208	67	22	hold	hold	NOUN
ejpam-5208	67	23	:	:	PUNCT
ejpam-5208	67	24	(	(	PUNCT
ejpam-5208	67	25	i	i	NOUN
ejpam-5208	67	26	)	)	PUNCT
ejpam-5208	67	27	a	a	PRON
ejpam-5208	67	28	⊆	⊆	NUM
ejpam-5208	67	29	(	(	PUNCT
ejpam-5208	67	30	i	i	NOUN
ejpam-5208	67	31	,	,	PUNCT
ejpam-5208	67	32	j)-ψgs	j)-ψgs	ADV
ejpam-5208	67	33	-	-	PUNCT
ejpam-5208	67	34	cl(a	cl(a	NUM
ejpam-5208	67	35	)	)	PUNCT
ejpam-5208	67	36	;	;	PUNCT
ejpam-5208	67	37	(	(	PUNCT
ejpam-5208	67	38	ii	ii	NOUN
ejpam-5208	67	39	)	)	PUNCT
ejpam-5208	67	40	(	(	PUNCT
ejpam-5208	67	41	i	i	NOUN
ejpam-5208	67	42	,	,	PUNCT
ejpam-5208	67	43	j)-ψgs	j)-ψgs	ADV
ejpam-5208	67	44	-	-	PUNCT
ejpam-5208	67	45	cl(a	cl(a	X
ejpam-5208	67	46	)	)	PUNCT
ejpam-5208	67	47	is	be	AUX
ejpam-5208	67	48	(	(	PUNCT
ejpam-5208	67	49	i	i	INTJ
ejpam-5208	67	50	,	,	PUNCT
ejpam-5208	67	51	j)-ψgs	j)-ψgs	ADV
ejpam-5208	67	52	-	-	PUNCT
ejpam-5208	67	53	closed	closed	ADJ
ejpam-5208	67	54	set	set	NOUN
ejpam-5208	67	55	;	;	PUNCT
ejpam-5208	67	56	and	and	CCONJ
ejpam-5208	67	57	(	(	PUNCT
ejpam-5208	67	58	iii	iii	X
ejpam-5208	67	59	)	)	PUNCT
ejpam-5208	67	60	if	if	SCONJ
ejpam-5208	67	61	a	a	DET
ejpam-5208	67	62	⊆	⊆	NUM
ejpam-5208	67	63	b	b	NOUN
ejpam-5208	67	64	such	such	DET
ejpam-5208	67	65	that	that	DET
ejpam-5208	67	66	b	b	NOUN
ejpam-5208	67	67	is	be	AUX
ejpam-5208	67	68	(	(	PUNCT
ejpam-5208	67	69	i	i	NOUN
ejpam-5208	67	70	,	,	PUNCT
ejpam-5208	67	71	j)-ψgs	j)-ψgs	ADV
ejpam-5208	67	72	-	-	PUNCT
ejpam-5208	67	73	closed	closed	ADJ
ejpam-5208	67	74	set	set	NOUN
ejpam-5208	67	75	,	,	PUNCT
ejpam-5208	67	76	then	then	ADV
ejpam-5208	67	77	(	(	PUNCT
ejpam-5208	67	78	i	i	NOUN
ejpam-5208	67	79	,	,	PUNCT
ejpam-5208	67	80	j)-ψgs	j)-ψgs	ADV
ejpam-5208	67	81	-	-	PUNCT
ejpam-5208	67	82	cl(a	cl(a	NUM
ejpam-5208	67	83	)	)	PUNCT
ejpam-5208	67	84	⊆	⊆	PROPN
ejpam-5208	67	85	b.	b.	NOUN
ejpam-5208	67	86	theorem	theorem	NOUN
ejpam-5208	67	87	2	2	X
ejpam-5208	67	88	.	.	PUNCT
ejpam-5208	68	1	let	let	AUX
ejpam-5208	68	2	(	(	PUNCT
ejpam-5208	68	3	x	x	NOUN
ejpam-5208	68	4	,	,	PUNCT
ejpam-5208	68	5	τ1	τ1	NOUN
ejpam-5208	68	6	,	,	PUNCT
ejpam-5208	68	7	τ2	τ2	PROPN
ejpam-5208	68	8	)	)	PUNCT
ejpam-5208	68	9	be	be	VERB
ejpam-5208	68	10	a	a	DET
ejpam-5208	68	11	bitopological	bitopological	ADJ
ejpam-5208	68	12	space	space	NOUN
ejpam-5208	68	13	and	and	CCONJ
ejpam-5208	68	14	a	a	DET
ejpam-5208	68	15	⊆	⊆	NUM
ejpam-5208	68	16	x.	x.	NOUN
ejpam-5208	68	17	a	a	DET
ejpam-5208	68	18	set	set	NOUN
ejpam-5208	68	19	a	a	PRON
ejpam-5208	68	20	is	be	AUX
ejpam-5208	68	21	(	(	PUNCT
ejpam-5208	68	22	i	i	PROPN
ejpam-5208	68	23	,	,	PUNCT
ejpam-5208	68	24	j)-ψgsclosed	j)-ψgsclosed	ADJ
ejpam-5208	68	25	set	set	NOUN
ejpam-5208	68	26	,	,	PUNCT
ejpam-5208	68	27	if	if	SCONJ
ejpam-5208	68	28	and	and	CCONJ
ejpam-5208	68	29	only	only	ADV
ejpam-5208	68	30	if	if	SCONJ
ejpam-5208	68	31	(	(	PUNCT
ejpam-5208	68	32	i	i	NOUN
ejpam-5208	68	33	,	,	PUNCT
ejpam-5208	68	34	j)-ψgs	j)-ψgs	ADV
ejpam-5208	68	35	-	-	PUNCT
ejpam-5208	68	36	cl(a	cl(a	NUM
ejpam-5208	68	37	)	)	PUNCT
ejpam-5208	68	38	=	=	SYM
ejpam-5208	68	39	a.	a.	PROPN
ejpam-5208	68	40	l.	l.	PROPN
ejpam-5208	68	41	m.	m.	PROPN
ejpam-5208	68	42	tutanes	tutane	NOUN
ejpam-5208	68	43	/	/	SYM
ejpam-5208	68	44	eur	eur	PROPN
ejpam-5208	68	45	.	.	PUNCT
ejpam-5208	69	1	j.	j.	PROPN
ejpam-5208	69	2	pure	pure	PROPN
ejpam-5208	69	3	appl	appl	PROPN
ejpam-5208	69	4	.	.	PROPN
ejpam-5208	69	5	math	math	PROPN
ejpam-5208	69	6	,	,	PUNCT
ejpam-5208	69	7	17	17	NUM
ejpam-5208	69	8	(	(	PUNCT
ejpam-5208	69	9	3	3	NUM
ejpam-5208	69	10	)	)	PUNCT
ejpam-5208	69	11	(	(	PUNCT
ejpam-5208	69	12	2024	2024	NUM
ejpam-5208	69	13	)	)	PUNCT
ejpam-5208	69	14	,	,	PUNCT
ejpam-5208	69	15	2173	2173	NUM
ejpam-5208	69	16	-	-	SYM
ejpam-5208	69	17	2181	2181	NUM
ejpam-5208	69	18	2176	2176	NUM
ejpam-5208	69	19	3	3	NUM
ejpam-5208	69	20	.	.	PUNCT
ejpam-5208	69	21	ψgs	ψgs	ADV
ejpam-5208	69	22	-	-	PUNCT
ejpam-5208	69	23	open	open	ADJ
ejpam-5208	69	24	function	function	NOUN
ejpam-5208	69	25	in	in	ADP
ejpam-5208	69	26	bts	bt	NOUN
ejpam-5208	69	27	in	in	ADP
ejpam-5208	69	28	this	this	DET
ejpam-5208	69	29	section	section	NOUN
ejpam-5208	69	30	ψgs	ψgs	ADV
ejpam-5208	69	31	-	-	PUNCT
ejpam-5208	69	32	open	open	ADJ
ejpam-5208	69	33	function	function	NOUN
ejpam-5208	69	34	is	be	AUX
ejpam-5208	69	35	introduced	introduce	VERB
ejpam-5208	69	36	in	in	ADP
ejpam-5208	69	37	bts	bt	NOUN
ejpam-5208	69	38	and	and	CCONJ
ejpam-5208	69	39	some	some	PRON
ejpam-5208	69	40	of	of	ADP
ejpam-5208	69	41	its	its	PRON
ejpam-5208	69	42	properties	property	NOUN
ejpam-5208	69	43	are	be	AUX
ejpam-5208	69	44	investigated	investigate	VERB
ejpam-5208	69	45	.	.	PUNCT
ejpam-5208	70	1	definition	definition	NOUN
ejpam-5208	70	2	4	4	NUM
ejpam-5208	70	3	.	.	PUNCT
ejpam-5208	71	1	let	let	VERB
ejpam-5208	71	2	(	(	PUNCT
ejpam-5208	71	3	x	x	NOUN
ejpam-5208	71	4	,	,	PUNCT
ejpam-5208	71	5	τ1	τ1	NOUN
ejpam-5208	71	6	,	,	PUNCT
ejpam-5208	71	7	τ2	τ2	NOUN
ejpam-5208	71	8	)	)	PUNCT
ejpam-5208	71	9	and	and	CCONJ
ejpam-5208	71	10	(	(	PUNCT
ejpam-5208	71	11	y	y	PROPN
ejpam-5208	71	12	,	,	PUNCT
ejpam-5208	71	13	σ1	σ1	PROPN
ejpam-5208	71	14	,	,	PUNCT
ejpam-5208	71	15	σ2	σ2	PROPN
ejpam-5208	71	16	)	)	PUNCT
ejpam-5208	71	17	be	be	VERB
ejpam-5208	71	18	two	two	NUM
ejpam-5208	71	19	bitopological	bitopological	ADJ
ejpam-5208	71	20	spaces	space	NOUN
ejpam-5208	71	21	.	.	PUNCT
ejpam-5208	72	1	a	a	DET
ejpam-5208	72	2	function	function	NOUN
ejpam-5208	72	3	f	f	NOUN
ejpam-5208	72	4	:	:	PUNCT
ejpam-5208	72	5	(	(	PUNCT
ejpam-5208	72	6	x	x	NOUN
ejpam-5208	72	7	,	,	PUNCT
ejpam-5208	72	8	τ1	τ1	NOUN
ejpam-5208	72	9	,	,	PUNCT
ejpam-5208	72	10	τ2	τ2	NOUN
ejpam-5208	72	11	)	)	PUNCT
ejpam-5208	72	12	→	→	SYM
ejpam-5208	72	13	(	(	PUNCT
ejpam-5208	72	14	y	y	PROPN
ejpam-5208	72	15	,	,	PUNCT
ejpam-5208	72	16	σ1	σ1	PROPN
ejpam-5208	72	17	,	,	PUNCT
ejpam-5208	72	18	σ2	σ2	PROPN
ejpam-5208	72	19	)	)	PUNCT
ejpam-5208	72	20	is	be	AUX
ejpam-5208	72	21	said	say	VERB
ejpam-5208	72	22	to	to	PART
ejpam-5208	72	23	be	be	AUX
ejpam-5208	72	24	an	an	DET
ejpam-5208	72	25	(	(	PUNCT
ejpam-5208	72	26	i	i	NOUN
ejpam-5208	72	27	,	,	PUNCT
ejpam-5208	72	28	j)-ψ	j)-ψ	PROPN
ejpam-5208	72	29	-	-	ADJ
ejpam-5208	72	30	generalized	generalize	VERB
ejpam-5208	72	31	semi	semi	ADV
ejpam-5208	72	32	open	open	ADJ
ejpam-5208	72	33	(	(	PUNCT
ejpam-5208	72	34	briefly	briefly	ADV
ejpam-5208	72	35	,	,	PUNCT
ejpam-5208	72	36	(	(	PUNCT
ejpam-5208	72	37	i	i	X
ejpam-5208	72	38	,	,	PUNCT
ejpam-5208	72	39	j)ψgs	j)ψgs	PROPN
ejpam-5208	72	40	-	-	PUNCT
ejpam-5208	72	41	open	open	ADJ
ejpam-5208	72	42	)	)	PUNCT
ejpam-5208	72	43	function	function	NOUN
ejpam-5208	72	44	if	if	SCONJ
ejpam-5208	72	45	for	for	ADP
ejpam-5208	72	46	every	every	DET
ejpam-5208	72	47	τi	τi	NOUN
ejpam-5208	72	48	-	-	PUNCT
ejpam-5208	72	49	open	open	NOUN
ejpam-5208	72	50	set	set	VERB
ejpam-5208	72	51	a	a	PRON
ejpam-5208	72	52	in	in	ADP
ejpam-5208	72	53	x	x	PROPN
ejpam-5208	72	54	,	,	PUNCT
ejpam-5208	72	55	f(a	f(a	PROPN
ejpam-5208	72	56	)	)	PUNCT
ejpam-5208	72	57	is	be	AUX
ejpam-5208	72	58	(	(	PUNCT
ejpam-5208	72	59	i	i	INTJ
ejpam-5208	72	60	,	,	PUNCT
ejpam-5208	72	61	j)-ψgs	j)-ψgs	ADV
ejpam-5208	72	62	-	-	ADJ
ejpam-5208	72	63	open	open	ADJ
ejpam-5208	72	64	set	set	NOUN
ejpam-5208	72	65	in	in	ADP
ejpam-5208	72	66	y	y	PROPN
ejpam-5208	72	67	,	,	PUNCT
ejpam-5208	72	68	where	where	SCONJ
ejpam-5208	72	69	i	i	PRON
ejpam-5208	72	70	∈	∈	PROPN
ejpam-5208	72	71	{	{	PUNCT
ejpam-5208	72	72	1	1	NUM
ejpam-5208	72	73	,	,	PUNCT
ejpam-5208	72	74	2	2	NUM
ejpam-5208	72	75	}	}	PUNCT
ejpam-5208	72	76	.	.	PUNCT
ejpam-5208	73	1	theorem	theorem	NOUN
ejpam-5208	73	2	3	3	X
ejpam-5208	73	3	.	.	PUNCT
ejpam-5208	74	1	let	let	VERB
ejpam-5208	74	2	(	(	PUNCT
ejpam-5208	74	3	x	x	NOUN
ejpam-5208	74	4	,	,	PUNCT
ejpam-5208	74	5	τ1	τ1	NOUN
ejpam-5208	74	6	,	,	PUNCT
ejpam-5208	74	7	τ2	τ2	NOUN
ejpam-5208	74	8	)	)	PUNCT
ejpam-5208	74	9	and	and	CCONJ
ejpam-5208	74	10	(	(	PUNCT
ejpam-5208	74	11	y	y	PROPN
ejpam-5208	74	12	,	,	PUNCT
ejpam-5208	74	13	σ1	σ1	PROPN
ejpam-5208	74	14	,	,	PUNCT
ejpam-5208	74	15	σ2	σ2	PROPN
ejpam-5208	74	16	)	)	PUNCT
ejpam-5208	74	17	be	be	AUX
ejpam-5208	74	18	two	two	NUM
ejpam-5208	74	19	bitopological	bitopological	ADJ
ejpam-5208	74	20	spaces	space	NOUN
ejpam-5208	74	21	.	.	PUNCT
ejpam-5208	75	1	a	a	DET
ejpam-5208	75	2	function	function	NOUN
ejpam-5208	75	3	f	f	NOUN
ejpam-5208	75	4	:	:	PUNCT
ejpam-5208	75	5	(	(	PUNCT
ejpam-5208	75	6	x	x	NOUN
ejpam-5208	75	7	,	,	PUNCT
ejpam-5208	75	8	τ1	τ1	NOUN
ejpam-5208	75	9	,	,	PUNCT
ejpam-5208	75	10	τ2	τ2	NOUN
ejpam-5208	75	11	)	)	PUNCT
ejpam-5208	75	12	→	→	SYM
ejpam-5208	75	13	(	(	PUNCT
ejpam-5208	75	14	y	y	PROPN
ejpam-5208	75	15	,	,	PUNCT
ejpam-5208	75	16	σ1	σ1	PROPN
ejpam-5208	75	17	,	,	PUNCT
ejpam-5208	75	18	σ2	σ2	PROPN
ejpam-5208	75	19	)	)	PUNCT
ejpam-5208	75	20	is	be	AUX
ejpam-5208	75	21	(	(	PUNCT
ejpam-5208	75	22	i	i	NOUN
ejpam-5208	75	23	,	,	PUNCT
ejpam-5208	75	24	j)-ψgs	j)-ψgs	ADV
ejpam-5208	75	25	-	-	PUNCT
ejpam-5208	75	26	open	open	ADJ
ejpam-5208	75	27	function	function	NOUN
ejpam-5208	75	28	if	if	SCONJ
ejpam-5208	75	29	and	and	CCONJ
ejpam-5208	75	30	only	only	ADV
ejpam-5208	75	31	if	if	SCONJ
ejpam-5208	75	32	for	for	ADP
ejpam-5208	75	33	every	every	DET
ejpam-5208	75	34	τi	τi	NOUN
ejpam-5208	75	35	-	-	PUNCT
ejpam-5208	75	36	open	open	NOUN
ejpam-5208	75	37	set	set	VERB
ejpam-5208	75	38	a	a	DET
ejpam-5208	75	39	in	in	ADP
ejpam-5208	75	40	x	x	PROPN
ejpam-5208	75	41	f(inti(a	f(inti(a	NOUN
ejpam-5208	75	42	)	)	PUNCT
ejpam-5208	75	43	)	)	PUNCT
ejpam-5208	76	1	=	=	SYM
ejpam-5208	76	2	(	(	PUNCT
ejpam-5208	76	3	i	i	INTJ
ejpam-5208	76	4	,	,	PUNCT
ejpam-5208	76	5	j)-ψgs	j)-ψgs	PROPN
ejpam-5208	76	6	-	-	PUNCT
ejpam-5208	76	7	int(f(a	int(f(a	NOUN
ejpam-5208	76	8	)	)	PUNCT
ejpam-5208	76	9	)	)	PUNCT
ejpam-5208	76	10	.	.	PUNCT
ejpam-5208	77	1	proof	proof	NOUN
ejpam-5208	77	2	.	.	PUNCT
ejpam-5208	78	1	let	let	VERB
ejpam-5208	78	2	f	f	PRON
ejpam-5208	78	3	be	be	AUX
ejpam-5208	78	4	(	(	PUNCT
ejpam-5208	78	5	i	i	NOUN
ejpam-5208	78	6	,	,	PUNCT
ejpam-5208	78	7	j)-ψgs	j)-ψgs	ADV
ejpam-5208	78	8	-	-	PUNCT
ejpam-5208	78	9	open	open	ADJ
ejpam-5208	78	10	function	function	NOUN
ejpam-5208	78	11	and	and	CCONJ
ejpam-5208	78	12	a	a	DET
ejpam-5208	78	13	be	be	NOUN
ejpam-5208	78	14	τi	τi	NOUN
ejpam-5208	78	15	-	-	PUNCT
ejpam-5208	78	16	open	open	ADJ
ejpam-5208	78	17	in	in	ADP
ejpam-5208	78	18	x.	x.	NOUN
ejpam-5208	78	19	it	it	PRON
ejpam-5208	78	20	follows	follow	VERB
ejpam-5208	78	21	that	that	SCONJ
ejpam-5208	78	22	f(a	f(a	NOUN
ejpam-5208	78	23	)	)	PUNCT
ejpam-5208	78	24	is	be	AUX
ejpam-5208	78	25	(	(	PUNCT
ejpam-5208	78	26	i	i	INTJ
ejpam-5208	78	27	,	,	PUNCT
ejpam-5208	78	28	j)-ψgs	j)-ψgs	ADV
ejpam-5208	78	29	-	-	ADJ
ejpam-5208	78	30	open	open	ADJ
ejpam-5208	78	31	set	set	NOUN
ejpam-5208	78	32	in	in	ADP
ejpam-5208	78	33	y	y	PROPN
ejpam-5208	78	34	where	where	SCONJ
ejpam-5208	78	35	i	i	PRON
ejpam-5208	78	36	,	,	PUNCT
ejpam-5208	78	37	j	j	PROPN
ejpam-5208	78	38	∈	∈	PROPN
ejpam-5208	78	39	{	{	PUNCT
ejpam-5208	78	40	1	1	NUM
ejpam-5208	78	41	,	,	PUNCT
ejpam-5208	78	42	2	2	NUM
ejpam-5208	78	43	}	}	PUNCT
ejpam-5208	78	44	.	.	PUNCT
ejpam-5208	79	1	since	since	SCONJ
ejpam-5208	79	2	a	a	PRON
ejpam-5208	79	3	is	be	AUX
ejpam-5208	79	4	τi	τi	NOUN
ejpam-5208	79	5	-	-	PUNCT
ejpam-5208	79	6	open	open	ADJ
ejpam-5208	79	7	,	,	PUNCT
ejpam-5208	79	8	inti(a	inti(a	NOUN
ejpam-5208	79	9	)	)	PUNCT
ejpam-5208	79	10	=	=	SYM
ejpam-5208	80	1	a	a	PRON
ejpam-5208	80	2	,	,	PUNCT
ejpam-5208	80	3	and	and	CCONJ
ejpam-5208	80	4	so	so	ADV
ejpam-5208	80	5	f(inti(a	f(inti(a	ADJ
ejpam-5208	80	6	)	)	PUNCT
ejpam-5208	80	7	)	)	PUNCT
ejpam-5208	81	1	=	=	SYM
ejpam-5208	81	2	f(a	f(a	PROPN
ejpam-5208	81	3	)	)	PUNCT
ejpam-5208	81	4	.	.	PUNCT
ejpam-5208	82	1	note	note	VERB
ejpam-5208	82	2	that	that	SCONJ
ejpam-5208	82	3	f(a	f(a	NOUN
ejpam-5208	82	4	)	)	PUNCT
ejpam-5208	82	5	is	be	AUX
ejpam-5208	82	6	(	(	PUNCT
ejpam-5208	82	7	i	i	INTJ
ejpam-5208	82	8	,	,	PUNCT
ejpam-5208	82	9	j)-ψgs	j)-ψgs	ADV
ejpam-5208	82	10	-	-	PUNCT
ejpam-5208	82	11	open	open	ADJ
ejpam-5208	82	12	set	set	NOUN
ejpam-5208	82	13	,	,	PUNCT
ejpam-5208	82	14	it	it	PRON
ejpam-5208	82	15	follows	follow	VERB
ejpam-5208	82	16	that	that	SCONJ
ejpam-5208	82	17	(	(	PUNCT
ejpam-5208	82	18	i	i	PRON
ejpam-5208	82	19	,	,	PUNCT
ejpam-5208	82	20	j)-ψgs	j)-ψgs	PROPN
ejpam-5208	82	21	-	-	PUNCT
ejpam-5208	82	22	int(f(a	int(f(a	NOUN
ejpam-5208	82	23	)	)	PUNCT
ejpam-5208	82	24	)	)	PUNCT
ejpam-5208	82	25	=	=	SYM
ejpam-5208	82	26	f(a	f(a	NOUN
ejpam-5208	82	27	)	)	PUNCT
ejpam-5208	82	28	,	,	PUNCT
ejpam-5208	82	29	and	and	CCONJ
ejpam-5208	82	30	hence	hence	ADV
ejpam-5208	82	31	f(inti(a	f(inti(a	ADJ
ejpam-5208	82	32	)	)	PUNCT
ejpam-5208	82	33	)	)	PUNCT
ejpam-5208	83	1	=	=	SYM
ejpam-5208	83	2	(	(	PUNCT
ejpam-5208	83	3	i	i	INTJ
ejpam-5208	83	4	,	,	PUNCT
ejpam-5208	83	5	j)-ψgs	j)-ψgs	PROPN
ejpam-5208	83	6	-	-	PUNCT
ejpam-5208	83	7	int(f(a	int(f(a	NOUN
ejpam-5208	83	8	)	)	PUNCT
ejpam-5208	83	9	)	)	PUNCT
ejpam-5208	83	10	.	.	PUNCT
ejpam-5208	84	1	conversely	conversely	ADV
ejpam-5208	84	2	,	,	PUNCT
ejpam-5208	84	3	suppose	suppose	VERB
ejpam-5208	84	4	f(inti(a	f(inti(a	NOUN
ejpam-5208	84	5	)	)	PUNCT
ejpam-5208	84	6	)	)	PUNCT
ejpam-5208	85	1	=	=	SYM
ejpam-5208	85	2	(	(	PUNCT
ejpam-5208	85	3	i	i	INTJ
ejpam-5208	85	4	,	,	PUNCT
ejpam-5208	85	5	j)-ψgs	j)-ψgs	PROPN
ejpam-5208	85	6	-	-	PUNCT
ejpam-5208	85	7	int(f(a	int(f(a	NOUN
ejpam-5208	85	8	)	)	PUNCT
ejpam-5208	85	9	)	)	PUNCT
ejpam-5208	86	1	and	and	CCONJ
ejpam-5208	86	2	let	let	VERB
ejpam-5208	86	3	a	a	PRON
ejpam-5208	86	4	be	be	AUX
ejpam-5208	86	5	τi	τi	VERB
ejpam-5208	86	6	-	-	PUNCT
ejpam-5208	86	7	open	open	ADJ
ejpam-5208	86	8	set	set	NOUN
ejpam-5208	86	9	in	in	ADP
ejpam-5208	86	10	x.	x.	NOUN
ejpam-5208	86	11	then	then	ADV
ejpam-5208	86	12	inti(a	inti(a	PROPN
ejpam-5208	86	13	)	)	PUNCT
ejpam-5208	86	14	=	=	SYM
ejpam-5208	86	15	a	a	PRON
ejpam-5208	86	16	,	,	PUNCT
ejpam-5208	86	17	and	and	CCONJ
ejpam-5208	86	18	so	so	ADV
ejpam-5208	86	19	f(inti(a	f(inti(a	ADJ
ejpam-5208	86	20	)	)	PUNCT
ejpam-5208	86	21	)	)	PUNCT
ejpam-5208	87	1	=	=	SYM
ejpam-5208	87	2	f(a	f(a	NOUN
ejpam-5208	87	3	)	)	PUNCT
ejpam-5208	87	4	.	.	PUNCT
ejpam-5208	88	1	it	it	PRON
ejpam-5208	88	2	follows	follow	VERB
ejpam-5208	88	3	that	that	SCONJ
ejpam-5208	88	4	,	,	PUNCT
ejpam-5208	88	5	(	(	PUNCT
ejpam-5208	88	6	i	i	NOUN
ejpam-5208	88	7	,	,	PUNCT
ejpam-5208	88	8	j)-ψgs	j)-ψgs	PROPN
ejpam-5208	88	9	-	-	PUNCT
ejpam-5208	88	10	int(f(a	int(f(a	NOUN
ejpam-5208	88	11	)	)	PUNCT
ejpam-5208	88	12	)	)	PUNCT
ejpam-5208	89	1	=	=	SYM
ejpam-5208	89	2	f(a	f(a	PROPN
ejpam-5208	89	3	)	)	PUNCT
ejpam-5208	89	4	.	.	PUNCT
ejpam-5208	90	1	thus	thus	ADV
ejpam-5208	90	2	,	,	PUNCT
ejpam-5208	90	3	f(a	f(a	PROPN
ejpam-5208	90	4	)	)	PUNCT
ejpam-5208	90	5	is	be	AUX
ejpam-5208	90	6	(	(	PUNCT
ejpam-5208	90	7	i	i	INTJ
ejpam-5208	90	8	,	,	PUNCT
ejpam-5208	90	9	j)-ψgs	j)-ψgs	ADV
ejpam-5208	90	10	-	-	ADJ
ejpam-5208	90	11	open	open	ADJ
ejpam-5208	90	12	set	set	VERB
ejpam-5208	90	13	by	by	ADP
ejpam-5208	90	14	theorem	theorem	NOUN
ejpam-5208	90	15	1	1	NUM
ejpam-5208	90	16	.	.	PUNCT
ejpam-5208	90	17	hence	hence	ADV
ejpam-5208	90	18	,	,	PUNCT
ejpam-5208	90	19	by	by	ADP
ejpam-5208	90	20	definition	definition	NOUN
ejpam-5208	90	21	4	4	NUM
ejpam-5208	90	22	,	,	PUNCT
ejpam-5208	90	23	f	f	PROPN
ejpam-5208	90	24	is	be	AUX
ejpam-5208	90	25	(	(	PUNCT
ejpam-5208	90	26	i	i	NOUN
ejpam-5208	90	27	,	,	PUNCT
ejpam-5208	90	28	j)-ψgs	j)-ψgs	ADV
ejpam-5208	90	29	-	-	PUNCT
ejpam-5208	90	30	open	open	ADJ
ejpam-5208	90	31	function	function	NOUN
ejpam-5208	90	32	.	.	PUNCT
ejpam-5208	91	1	theorem	theorem	ADJ
ejpam-5208	91	2	4	4	NUM
ejpam-5208	91	3	.	.	PUNCT
ejpam-5208	92	1	let	let	VERB
ejpam-5208	92	2	(	(	PUNCT
ejpam-5208	92	3	x	x	NOUN
ejpam-5208	92	4	,	,	PUNCT
ejpam-5208	92	5	τ1	τ1	NOUN
ejpam-5208	92	6	,	,	PUNCT
ejpam-5208	92	7	τ2	τ2	NOUN
ejpam-5208	92	8	)	)	PUNCT
ejpam-5208	92	9	and	and	CCONJ
ejpam-5208	92	10	(	(	PUNCT
ejpam-5208	92	11	y	y	PROPN
ejpam-5208	92	12	,	,	PUNCT
ejpam-5208	92	13	σ1	σ1	PROPN
ejpam-5208	92	14	,	,	PUNCT
ejpam-5208	92	15	σ2	σ2	PROPN
ejpam-5208	92	16	)	)	PUNCT
ejpam-5208	92	17	be	be	AUX
ejpam-5208	92	18	two	two	NUM
ejpam-5208	92	19	bitopological	bitopological	ADJ
ejpam-5208	92	20	spaces	space	NOUN
ejpam-5208	92	21	.	.	PUNCT
ejpam-5208	93	1	a	a	DET
ejpam-5208	93	2	function	function	NOUN
ejpam-5208	93	3	f	f	NOUN
ejpam-5208	93	4	:	:	PUNCT
ejpam-5208	93	5	(	(	PUNCT
ejpam-5208	93	6	x	x	NOUN
ejpam-5208	93	7	,	,	PUNCT
ejpam-5208	93	8	τ1	τ1	NOUN
ejpam-5208	93	9	,	,	PUNCT
ejpam-5208	93	10	τ2	τ2	NOUN
ejpam-5208	93	11	)	)	PUNCT
ejpam-5208	93	12	→	→	SYM
ejpam-5208	93	13	(	(	PUNCT
ejpam-5208	93	14	y	y	PROPN
ejpam-5208	93	15	,	,	PUNCT
ejpam-5208	93	16	σ1	σ1	PROPN
ejpam-5208	93	17	,	,	PUNCT
ejpam-5208	93	18	σ2	σ2	PROPN
ejpam-5208	93	19	)	)	PUNCT
ejpam-5208	93	20	is	be	AUX
ejpam-5208	93	21	(	(	PUNCT
ejpam-5208	93	22	i	i	NOUN
ejpam-5208	93	23	,	,	PUNCT
ejpam-5208	93	24	j)-ψgs	j)-ψgs	ADV
ejpam-5208	93	25	-	-	PUNCT
ejpam-5208	93	26	open	open	ADJ
ejpam-5208	93	27	function	function	NOUN
ejpam-5208	93	28	if	if	SCONJ
ejpam-5208	93	29	and	and	CCONJ
ejpam-5208	93	30	only	only	ADV
ejpam-5208	93	31	if	if	SCONJ
ejpam-5208	93	32	for	for	ADP
ejpam-5208	93	33	any	any	DET
ejpam-5208	93	34	subset	subset	NOUN
ejpam-5208	93	35	b	b	PROPN
ejpam-5208	93	36	of	of	ADP
ejpam-5208	93	37	y	y	PROPN
ejpam-5208	93	38	and	and	CCONJ
ejpam-5208	93	39	for	for	ADP
ejpam-5208	93	40	any	any	DET
ejpam-5208	93	41	τi	τi	NOUN
ejpam-5208	93	42	-	-	PUNCT
ejpam-5208	93	43	closed	closed	ADJ
ejpam-5208	93	44	set	set	NOUN
ejpam-5208	93	45	a	a	PRON
ejpam-5208	93	46	of	of	ADP
ejpam-5208	93	47	x	x	SYM
ejpam-5208	93	48	containing	contain	VERB
ejpam-5208	93	49	f−1(b	f−1(b	PROPN
ejpam-5208	93	50	)	)	PUNCT
ejpam-5208	93	51	there	there	PRON
ejpam-5208	93	52	exists	exist	VERB
ejpam-5208	93	53	an	an	DET
ejpam-5208	93	54	(	(	PUNCT
ejpam-5208	93	55	i	i	NOUN
ejpam-5208	93	56	,	,	PUNCT
ejpam-5208	93	57	j)-ψgs	j)-ψgs	ADV
ejpam-5208	93	58	-	-	PUNCT
ejpam-5208	93	59	closet	closet	ADJ
ejpam-5208	93	60	set	set	NOUN
ejpam-5208	93	61	c	c	PROPN
ejpam-5208	93	62	of	of	ADP
ejpam-5208	93	63	y	y	PROPN
ejpam-5208	93	64	containing	contain	VERB
ejpam-5208	93	65	b	b	PROPN
ejpam-5208	93	66	such	such	ADJ
ejpam-5208	93	67	that	that	DET
ejpam-5208	93	68	f−1(c	f−1(c	PROPN
ejpam-5208	93	69	)	)	PUNCT
ejpam-5208	93	70	⊆	⊆	NUM
ejpam-5208	93	71	a.	a.	NOUN
ejpam-5208	93	72	proof	proof	NOUN
ejpam-5208	93	73	.	.	PUNCT
ejpam-5208	94	1	let	let	VERB
ejpam-5208	94	2	f	f	PRON
ejpam-5208	94	3	be	be	AUX
ejpam-5208	94	4	(	(	PUNCT
ejpam-5208	94	5	i	i	NOUN
ejpam-5208	94	6	,	,	PUNCT
ejpam-5208	94	7	j)-ψgs	j)-ψgs	ADV
ejpam-5208	94	8	-	-	PUNCT
ejpam-5208	94	9	open	open	ADJ
ejpam-5208	94	10	function	function	NOUN
ejpam-5208	94	11	,	,	PUNCT
ejpam-5208	94	12	b	b	PROPN
ejpam-5208	94	13	⊆	⊆	NUM
ejpam-5208	94	14	y	y	PROPN
ejpam-5208	94	15	,	,	PUNCT
ejpam-5208	94	16	and	and	CCONJ
ejpam-5208	94	17	a	a	DET
ejpam-5208	94	18	be	be	AUX
ejpam-5208	94	19	τi	τi	NOUN
ejpam-5208	94	20	-	-	PUNCT
ejpam-5208	94	21	closed	close	VERB
ejpam-5208	94	22	set	set	VERB
ejpam-5208	94	23	ofx	ofx	NOUN
ejpam-5208	94	24	containing	contain	VERB
ejpam-5208	94	25	f−1(b	f−1(b	PROPN
ejpam-5208	94	26	)	)	PUNCT
ejpam-5208	94	27	.	.	PUNCT
ejpam-5208	95	1	take	take	VERB
ejpam-5208	95	2	c	c	NOUN
ejpam-5208	95	3	=	=	SYM
ejpam-5208	95	4	y	y	PROPN
ejpam-5208	95	5	∖f(x∖a	∖f(x∖a	PROPN
ejpam-5208	95	6	)	)	PUNCT
ejpam-5208	95	7	and	and	CCONJ
ejpam-5208	95	8	note	note	VERB
ejpam-5208	95	9	that	that	SCONJ
ejpam-5208	95	10	f−1(b	f−1(b	PROPN
ejpam-5208	95	11	)	)	PUNCT
ejpam-5208	96	1	⊆	⊆	NUM
ejpam-5208	96	2	a.	a.	NOUN
ejpam-5208	96	3	these	these	PRON
ejpam-5208	96	4	imply	imply	VERB
ejpam-5208	96	5	that	that	SCONJ
ejpam-5208	96	6	b	b	PROPN
ejpam-5208	96	7	⊆	⊆	NUM
ejpam-5208	96	8	c.	c.	NOUN
ejpam-5208	96	9	since	since	SCONJ
ejpam-5208	96	10	f	f	PROPN
ejpam-5208	96	11	is	be	AUX
ejpam-5208	96	12	(	(	PUNCT
ejpam-5208	96	13	i	i	NOUN
ejpam-5208	96	14	,	,	PUNCT
ejpam-5208	96	15	j)-ψgs	j)-ψgs	ADV
ejpam-5208	96	16	-	-	PUNCT
ejpam-5208	96	17	open	open	ADJ
ejpam-5208	96	18	function	function	NOUN
ejpam-5208	96	19	and	and	CCONJ
ejpam-5208	96	20	x∖a	x∖a	PROPN
ejpam-5208	96	21	is	be	AUX
ejpam-5208	96	22	τi	τi	ADJ
ejpam-5208	96	23	-	-	PUNCT
ejpam-5208	96	24	open	open	ADJ
ejpam-5208	96	25	set	set	NOUN
ejpam-5208	96	26	,	,	PUNCT
ejpam-5208	96	27	f(x∖a	f(x∖a	PROPN
ejpam-5208	96	28	)	)	PUNCT
ejpam-5208	96	29	is	be	AUX
ejpam-5208	96	30	(	(	PUNCT
ejpam-5208	96	31	i	i	NOUN
ejpam-5208	96	32	,	,	PUNCT
ejpam-5208	96	33	j)-ψgs	j)-ψgs	ADV
ejpam-5208	96	34	-	-	PUNCT
ejpam-5208	96	35	open	open	ADJ
ejpam-5208	96	36	in	in	ADP
ejpam-5208	96	37	y	y	PROPN
ejpam-5208	96	38	.	.	PUNCT
ejpam-5208	97	1	hence	hence	ADV
ejpam-5208	97	2	c	c	PROPN
ejpam-5208	97	3	is	be	AUX
ejpam-5208	97	4	(	(	PUNCT
ejpam-5208	97	5	i	i	NOUN
ejpam-5208	97	6	,	,	PUNCT
ejpam-5208	97	7	j)-ψgs	j)-ψgs	ADV
ejpam-5208	97	8	-	-	PUNCT
ejpam-5208	97	9	closed	closed	ADJ
ejpam-5208	97	10	set	set	NOUN
ejpam-5208	97	11	of	of	ADP
ejpam-5208	97	12	y	y	PROPN
ejpam-5208	97	13	.	.	PUNCT
ejpam-5208	98	1	moreover	moreover	ADV
ejpam-5208	98	2	,	,	PUNCT
ejpam-5208	98	3	f−1(c	f−1(c	PROPN
ejpam-5208	98	4	)	)	PUNCT
ejpam-5208	99	1	⊆	⊆	NUM
ejpam-5208	99	2	a.	a.	NOUN
ejpam-5208	99	3	conversely	conversely	ADV
ejpam-5208	99	4	,	,	PUNCT
ejpam-5208	99	5	let	let	VERB
ejpam-5208	99	6	g	g	PRON
ejpam-5208	99	7	be	be	AUX
ejpam-5208	99	8	τi	τi	VERB
ejpam-5208	99	9	-	-	PUNCT
ejpam-5208	99	10	open	open	ADJ
ejpam-5208	99	11	set	set	NOUN
ejpam-5208	99	12	in	in	ADP
ejpam-5208	99	13	x.	x.	NOUN
ejpam-5208	99	14	take	take	VERB
ejpam-5208	99	15	b	b	NOUN
ejpam-5208	99	16	=	=	SYM
ejpam-5208	99	17	y	y	PROPN
ejpam-5208	99	18	∖f(g	∖f(g	PROPN
ejpam-5208	99	19	)	)	PUNCT
ejpam-5208	99	20	.	.	PUNCT
ejpam-5208	100	1	then	then	ADV
ejpam-5208	100	2	x∖g	x∖g	PROPN
ejpam-5208	100	3	is	be	AUX
ejpam-5208	100	4	τi	τi	ADV
ejpam-5208	100	5	-	-	PUNCT
ejpam-5208	100	6	closed	close	VERB
ejpam-5208	100	7	set	set	NOUN
ejpam-5208	100	8	in	in	ADP
ejpam-5208	100	9	x	x	INTJ
ejpam-5208	100	10	such	such	ADJ
ejpam-5208	100	11	that	that	DET
ejpam-5208	100	12	f−1(b	f−1(b	PROPN
ejpam-5208	100	13	)	)	PUNCT
ejpam-5208	100	14	⊆	⊆	NUM
ejpam-5208	100	15	x∖g	x∖g	PROPN
ejpam-5208	100	16	.	.	PUNCT
ejpam-5208	101	1	by	by	ADP
ejpam-5208	101	2	hypothesis	hypothesis	NOUN
ejpam-5208	101	3	,	,	PUNCT
ejpam-5208	101	4	there	there	PRON
ejpam-5208	101	5	exists	exist	VERB
ejpam-5208	101	6	(	(	PUNCT
ejpam-5208	101	7	i	i	PRON
ejpam-5208	101	8	,	,	PUNCT
ejpam-5208	101	9	j)-ψgs	j)-ψgs	ADV
ejpam-5208	101	10	-	-	PUNCT
ejpam-5208	101	11	closed	closed	ADJ
ejpam-5208	101	12	set	set	ADJ
ejpam-5208	101	13	c	c	PROPN
ejpam-5208	101	14	of	of	ADP
ejpam-5208	101	15	y	y	PROPN
ejpam-5208	101	16	containing	contain	VERB
ejpam-5208	101	17	b	b	PROPN
ejpam-5208	101	18	such	such	ADJ
ejpam-5208	101	19	that	that	DET
ejpam-5208	101	20	f−1(c	f−1(c	PROPN
ejpam-5208	101	21	)	)	PUNCT
ejpam-5208	101	22	⊆	⊆	NUM
ejpam-5208	101	23	x∖g	x∖g	PROPN
ejpam-5208	101	24	.	.	PUNCT
ejpam-5208	102	1	thus	thus	ADV
ejpam-5208	102	2	,	,	PUNCT
ejpam-5208	102	3	f(g	f(g	PROPN
ejpam-5208	102	4	)	)	PUNCT
ejpam-5208	102	5	⊆	⊆	NUM
ejpam-5208	102	6	y∖c	y∖c	PROPN
ejpam-5208	102	7	.	.	PUNCT
ejpam-5208	103	1	note	note	VERB
ejpam-5208	103	2	that	that	SCONJ
ejpam-5208	103	3	b	b	X
ejpam-5208	103	4	⊆	⊆	NUM
ejpam-5208	103	5	c	c	NOUN
ejpam-5208	103	6	,	,	PUNCT
ejpam-5208	103	7	and	and	CCONJ
ejpam-5208	103	8	so	so	ADV
ejpam-5208	103	9	y∖c	y∖c	PROPN
ejpam-5208	103	10	⊆	⊆	NUM
ejpam-5208	103	11	y∖b	y∖b	PROPN
ejpam-5208	103	12	=	=	PUNCT
ejpam-5208	103	13	f(g	f(g	PROPN
ejpam-5208	103	14	)	)	PUNCT
ejpam-5208	103	15	.	.	PUNCT
ejpam-5208	104	1	now	now	ADV
ejpam-5208	104	2	,	,	PUNCT
ejpam-5208	104	3	f(g	f(g	PROPN
ejpam-5208	104	4	)	)	PUNCT
ejpam-5208	104	5	⊆	⊆	NUM
ejpam-5208	104	6	y	y	PROPN
ejpam-5208	104	7	∖c	∖c	PROPN
ejpam-5208	104	8	and	and	CCONJ
ejpam-5208	104	9	y	y	PROPN
ejpam-5208	104	10	∖c	∖c	PROPN
ejpam-5208	104	11	⊆	⊆	NUM
ejpam-5208	104	12	f(g	f(g	NOUN
ejpam-5208	104	13	)	)	PUNCT
ejpam-5208	104	14	.	.	PUNCT
ejpam-5208	105	1	hence	hence	ADV
ejpam-5208	105	2	,	,	PUNCT
ejpam-5208	105	3	f(g	f(g	PROPN
ejpam-5208	105	4	)	)	PUNCT
ejpam-5208	105	5	=	=	SYM
ejpam-5208	105	6	y	y	PROPN
ejpam-5208	105	7	∖c	∖c	PROPN
ejpam-5208	105	8	,	,	PUNCT
ejpam-5208	105	9	which	which	PRON
ejpam-5208	105	10	is	be	AUX
ejpam-5208	105	11	(	(	PUNCT
ejpam-5208	105	12	i	i	NOUN
ejpam-5208	105	13	,	,	PUNCT
ejpam-5208	105	14	j)-ψgs	j)-ψgs	ADV
ejpam-5208	105	15	-	-	ADJ
ejpam-5208	105	16	open	open	ADJ
ejpam-5208	105	17	set	set	NOUN
ejpam-5208	105	18	in	in	ADP
ejpam-5208	105	19	y	y	PROPN
ejpam-5208	105	20	.	.	PUNCT
ejpam-5208	106	1	therefore	therefore	ADV
ejpam-5208	106	2	,	,	PUNCT
ejpam-5208	106	3	f	f	PROPN
ejpam-5208	106	4	is	be	AUX
ejpam-5208	106	5	(	(	PUNCT
ejpam-5208	106	6	i	i	NOUN
ejpam-5208	106	7	,	,	PUNCT
ejpam-5208	106	8	j)-ψgs	j)-ψgs	ADV
ejpam-5208	106	9	-	-	PUNCT
ejpam-5208	106	10	open	open	ADJ
ejpam-5208	106	11	function	function	NOUN
ejpam-5208	106	12	.	.	PUNCT
ejpam-5208	107	1	theorem	theorem	NOUN
ejpam-5208	107	2	5	5	NUM
ejpam-5208	107	3	.	.	PUNCT
ejpam-5208	108	1	let	let	VERB
ejpam-5208	108	2	(	(	PUNCT
ejpam-5208	108	3	x	x	NOUN
ejpam-5208	108	4	,	,	PUNCT
ejpam-5208	108	5	τ1	τ1	NOUN
ejpam-5208	108	6	,	,	PUNCT
ejpam-5208	108	7	τ2	τ2	NOUN
ejpam-5208	108	8	)	)	PUNCT
ejpam-5208	108	9	,	,	PUNCT
ejpam-5208	108	10	(	(	PUNCT
ejpam-5208	108	11	y	y	NOUN
ejpam-5208	108	12	,	,	PUNCT
ejpam-5208	108	13	µ1	µ1	PROPN
ejpam-5208	108	14	,	,	PUNCT
ejpam-5208	108	15	µ2	µ2	PROPN
ejpam-5208	108	16	)	)	PUNCT
ejpam-5208	108	17	,	,	PUNCT
ejpam-5208	108	18	and	and	CCONJ
ejpam-5208	108	19	(	(	PUNCT
ejpam-5208	108	20	z	z	PROPN
ejpam-5208	108	21	,	,	PUNCT
ejpam-5208	108	22	σ1	σ1	PROPN
ejpam-5208	108	23	,	,	PUNCT
ejpam-5208	108	24	σ2	σ2	PROPN
ejpam-5208	108	25	)	)	PUNCT
ejpam-5208	108	26	be	be	VERB
ejpam-5208	108	27	three	three	NUM
ejpam-5208	108	28	bitopological	bitopological	ADJ
ejpam-5208	108	29	spaces	space	NOUN
ejpam-5208	108	30	.	.	PUNCT
ejpam-5208	109	1	if	if	SCONJ
ejpam-5208	109	2	f	f	PROPN
ejpam-5208	109	3	:	:	PUNCT
ejpam-5208	109	4	(	(	PUNCT
ejpam-5208	109	5	x	x	NOUN
ejpam-5208	109	6	,	,	PUNCT
ejpam-5208	109	7	τ1	τ1	NOUN
ejpam-5208	109	8	,	,	PUNCT
ejpam-5208	109	9	τ2	τ2	NOUN
ejpam-5208	109	10	)	)	PUNCT
ejpam-5208	109	11	→	→	SYM
ejpam-5208	109	12	(	(	PUNCT
ejpam-5208	109	13	y	y	PROPN
ejpam-5208	109	14	,	,	PUNCT
ejpam-5208	109	15	µ1	µ1	PROPN
ejpam-5208	109	16	,	,	PUNCT
ejpam-5208	109	17	µ2	µ2	PROPN
ejpam-5208	109	18	)	)	PUNCT
ejpam-5208	109	19	is	be	AUX
ejpam-5208	109	20	τi	τi	ADJ
ejpam-5208	109	21	-	-	PUNCT
ejpam-5208	109	22	open	open	ADJ
ejpam-5208	109	23	function	function	NOUN
ejpam-5208	109	24	and	and	CCONJ
ejpam-5208	109	25	g	g	NOUN
ejpam-5208	109	26	:	:	PUNCT
ejpam-5208	109	27	(	(	PUNCT
ejpam-5208	109	28	y	y	PROPN
ejpam-5208	109	29	,	,	PUNCT
ejpam-5208	109	30	µ1	µ1	PROPN
ejpam-5208	109	31	,	,	PUNCT
ejpam-5208	109	32	µ2	µ2	PROPN
ejpam-5208	109	33	)	)	PUNCT
ejpam-5208	109	34	→	→	SYM
ejpam-5208	109	35	(	(	PUNCT
ejpam-5208	109	36	z	z	PROPN
ejpam-5208	109	37	,	,	PUNCT
ejpam-5208	109	38	σ1	σ1	PROPN
ejpam-5208	109	39	,	,	PUNCT
ejpam-5208	109	40	σ2	σ2	PROPN
ejpam-5208	109	41	)	)	PUNCT
ejpam-5208	109	42	is	be	AUX
ejpam-5208	109	43	(	(	PUNCT
ejpam-5208	109	44	i	i	X
ejpam-5208	109	45	,	,	PUNCT
ejpam-5208	109	46	j)ψgs	j)ψgs	PROPN
ejpam-5208	109	47	-	-	PUNCT
ejpam-5208	109	48	open	open	ADJ
ejpam-5208	109	49	function	function	NOUN
ejpam-5208	109	50	,	,	PUNCT
ejpam-5208	109	51	then	then	ADV
ejpam-5208	109	52	g	g	PROPN
ejpam-5208	109	53	◦	◦	NOUN
ejpam-5208	109	54	f	f	X
ejpam-5208	109	55	:	:	PUNCT
ejpam-5208	109	56	(	(	PUNCT
ejpam-5208	109	57	x	x	NOUN
ejpam-5208	109	58	,	,	PUNCT
ejpam-5208	109	59	τ1	τ1	NOUN
ejpam-5208	109	60	,	,	PUNCT
ejpam-5208	109	61	τ2	τ2	NOUN
ejpam-5208	109	62	)	)	PUNCT
ejpam-5208	109	63	→	→	SYM
ejpam-5208	109	64	(	(	PUNCT
ejpam-5208	109	65	z	z	PROPN
ejpam-5208	109	66	,	,	PUNCT
ejpam-5208	109	67	σ1	σ1	PROPN
ejpam-5208	109	68	,	,	PUNCT
ejpam-5208	109	69	σ2	σ2	PROPN
ejpam-5208	109	70	)	)	PUNCT
ejpam-5208	109	71	is	be	AUX
ejpam-5208	109	72	(	(	PUNCT
ejpam-5208	109	73	i	i	NOUN
ejpam-5208	109	74	,	,	PUNCT
ejpam-5208	109	75	j)-ψgs	j)-ψgs	ADV
ejpam-5208	109	76	-	-	PUNCT
ejpam-5208	109	77	open	open	ADJ
ejpam-5208	109	78	function	function	NOUN
ejpam-5208	109	79	.	.	PUNCT
ejpam-5208	110	1	l.	l.	PROPN
ejpam-5208	110	2	m.	m.	PROPN
ejpam-5208	110	3	tutanes	tutane	NOUN
ejpam-5208	110	4	/	/	SYM
ejpam-5208	110	5	eur	eur	PROPN
ejpam-5208	110	6	.	.	PUNCT
ejpam-5208	111	1	j.	j.	PROPN
ejpam-5208	111	2	pure	pure	PROPN
ejpam-5208	111	3	appl	appl	PROPN
ejpam-5208	111	4	.	.	PROPN
ejpam-5208	111	5	math	math	PROPN
ejpam-5208	111	6	,	,	PUNCT
ejpam-5208	111	7	17	17	NUM
ejpam-5208	111	8	(	(	PUNCT
ejpam-5208	111	9	3	3	NUM
ejpam-5208	111	10	)	)	PUNCT
ejpam-5208	111	11	(	(	PUNCT
ejpam-5208	111	12	2024	2024	NUM
ejpam-5208	111	13	)	)	PUNCT
ejpam-5208	111	14	,	,	PUNCT
ejpam-5208	111	15	2173	2173	NUM
ejpam-5208	111	16	-	-	SYM
ejpam-5208	111	17	2181	2181	NUM
ejpam-5208	111	18	2177	2177	NUM
ejpam-5208	111	19	proof	proof	NOUN
ejpam-5208	111	20	.	.	PUNCT
ejpam-5208	112	1	let	let	VERB
ejpam-5208	112	2	f	f	PRON
ejpam-5208	112	3	be	be	AUX
ejpam-5208	112	4	τi	τi	VERB
ejpam-5208	112	5	-	-	PUNCT
ejpam-5208	112	6	open	open	ADJ
ejpam-5208	112	7	function	function	NOUN
ejpam-5208	112	8	.	.	PUNCT
ejpam-5208	113	1	then	then	ADV
ejpam-5208	113	2	f(a	f(a	PROPN
ejpam-5208	113	3	)	)	PUNCT
ejpam-5208	113	4	is	be	AUX
ejpam-5208	113	5	τi	τi	ADJ
ejpam-5208	113	6	-	-	PUNCT
ejpam-5208	113	7	open	open	ADJ
ejpam-5208	113	8	in	in	ADP
ejpam-5208	113	9	y	y	PROPN
ejpam-5208	113	10	for	for	ADP
ejpam-5208	113	11	every	every	DET
ejpam-5208	113	12	τi	τi	NOUN
ejpam-5208	113	13	-	-	PUNCT
ejpam-5208	113	14	open	open	NOUN
ejpam-5208	113	15	set	set	NOUN
ejpam-5208	113	16	a	a	PRON
ejpam-5208	113	17	in	in	ADP
ejpam-5208	113	18	x.	x.	NOUN
ejpam-5208	113	19	since	since	SCONJ
ejpam-5208	113	20	g	g	PROPN
ejpam-5208	113	21	is	be	AUX
ejpam-5208	113	22	(	(	PUNCT
ejpam-5208	113	23	i	i	NOUN
ejpam-5208	113	24	,	,	PUNCT
ejpam-5208	113	25	j)-ψgs	j)-ψgs	ADV
ejpam-5208	113	26	-	-	PUNCT
ejpam-5208	113	27	open	open	ADJ
ejpam-5208	113	28	function	function	NOUN
ejpam-5208	113	29	,	,	PUNCT
ejpam-5208	113	30	it	it	PRON
ejpam-5208	113	31	follows	follow	VERB
ejpam-5208	113	32	that	that	PRON
ejpam-5208	113	33	g(f(a	g(f(a	NOUN
ejpam-5208	113	34	)	)	PUNCT
ejpam-5208	113	35	)	)	PUNCT
ejpam-5208	114	1	=	=	PRON
ejpam-5208	114	2	(	(	PUNCT
ejpam-5208	114	3	g	g	NOUN
ejpam-5208	114	4	◦	◦	NOUN
ejpam-5208	114	5	f)(a	f)(a	NOUN
ejpam-5208	114	6	)	)	PUNCT
ejpam-5208	114	7	is	be	AUX
ejpam-5208	114	8	(	(	PUNCT
ejpam-5208	114	9	i	i	PRON
ejpam-5208	114	10	,	,	PUNCT
ejpam-5208	114	11	j)-ψgsopen	j)-ψgsopen	PUNCT
ejpam-5208	114	12	set	set	VERB
ejpam-5208	114	13	in	in	ADP
ejpam-5208	114	14	z.	z.	PROPN
ejpam-5208	114	15	hence	hence	ADV
ejpam-5208	114	16	g	g	PROPN
ejpam-5208	114	17	◦	◦	PROPN
ejpam-5208	114	18	f	f	X
ejpam-5208	114	19	is	be	AUX
ejpam-5208	114	20	(	(	PUNCT
ejpam-5208	114	21	i	i	NOUN
ejpam-5208	114	22	,	,	PUNCT
ejpam-5208	114	23	j)-ψgs	j)-ψgs	ADV
ejpam-5208	114	24	-	-	PUNCT
ejpam-5208	114	25	open	open	ADJ
ejpam-5208	114	26	function	function	NOUN
ejpam-5208	114	27	.	.	PUNCT
ejpam-5208	115	1	4	4	X
ejpam-5208	115	2	.	.	X
ejpam-5208	115	3	ψgs	ψgs	ADV
ejpam-5208	115	4	-	-	PUNCT
ejpam-5208	115	5	closed	close	VERB
ejpam-5208	115	6	function	function	NOUN
ejpam-5208	115	7	in	in	ADP
ejpam-5208	115	8	bts	bt	NOUN
ejpam-5208	115	9	in	in	ADP
ejpam-5208	115	10	this	this	DET
ejpam-5208	115	11	section	section	NOUN
ejpam-5208	115	12	ψgs	ψgs	ADV
ejpam-5208	115	13	-	-	PUNCT
ejpam-5208	115	14	closed	close	VERB
ejpam-5208	115	15	function	function	NOUN
ejpam-5208	115	16	is	be	AUX
ejpam-5208	115	17	presented	present	VERB
ejpam-5208	115	18	in	in	ADP
ejpam-5208	115	19	bts	bt	NOUN
ejpam-5208	115	20	and	and	CCONJ
ejpam-5208	115	21	some	some	PRON
ejpam-5208	115	22	of	of	ADP
ejpam-5208	115	23	its	its	PRON
ejpam-5208	115	24	properties	property	NOUN
ejpam-5208	115	25	are	be	AUX
ejpam-5208	115	26	explored	explore	VERB
ejpam-5208	115	27	.	.	PUNCT
ejpam-5208	116	1	definition	definition	NOUN
ejpam-5208	116	2	5	5	NUM
ejpam-5208	116	3	.	.	PUNCT
ejpam-5208	117	1	let	let	VERB
ejpam-5208	117	2	(	(	PUNCT
ejpam-5208	117	3	x	x	NOUN
ejpam-5208	117	4	,	,	PUNCT
ejpam-5208	117	5	τ1	τ1	NOUN
ejpam-5208	117	6	,	,	PUNCT
ejpam-5208	117	7	τ2	τ2	NOUN
ejpam-5208	117	8	)	)	PUNCT
ejpam-5208	117	9	and	and	CCONJ
ejpam-5208	117	10	(	(	PUNCT
ejpam-5208	117	11	y	y	PROPN
ejpam-5208	117	12	,	,	PUNCT
ejpam-5208	117	13	σ1	σ1	PROPN
ejpam-5208	117	14	,	,	PUNCT
ejpam-5208	117	15	σ2	σ2	PROPN
ejpam-5208	117	16	)	)	PUNCT
ejpam-5208	117	17	be	be	VERB
ejpam-5208	117	18	two	two	NUM
ejpam-5208	117	19	bitopological	bitopological	ADJ
ejpam-5208	117	20	spaces	space	NOUN
ejpam-5208	117	21	.	.	PUNCT
ejpam-5208	118	1	a	a	DET
ejpam-5208	118	2	function	function	NOUN
ejpam-5208	118	3	f	f	NOUN
ejpam-5208	118	4	:	:	PUNCT
ejpam-5208	118	5	(	(	PUNCT
ejpam-5208	118	6	x	x	NOUN
ejpam-5208	118	7	,	,	PUNCT
ejpam-5208	118	8	τ1	τ1	NOUN
ejpam-5208	118	9	,	,	PUNCT
ejpam-5208	118	10	τ2	τ2	NOUN
ejpam-5208	118	11	)	)	PUNCT
ejpam-5208	118	12	→	→	SYM
ejpam-5208	118	13	(	(	PUNCT
ejpam-5208	118	14	y	y	PROPN
ejpam-5208	118	15	,	,	PUNCT
ejpam-5208	118	16	σ1	σ1	PROPN
ejpam-5208	118	17	,	,	PUNCT
ejpam-5208	118	18	σ2	σ2	PROPN
ejpam-5208	118	19	)	)	PUNCT
ejpam-5208	118	20	is	be	AUX
ejpam-5208	118	21	said	say	VERB
ejpam-5208	118	22	to	to	PART
ejpam-5208	118	23	be	be	AUX
ejpam-5208	118	24	an	an	DET
ejpam-5208	118	25	(	(	PUNCT
ejpam-5208	118	26	i	i	NOUN
ejpam-5208	118	27	,	,	PUNCT
ejpam-5208	118	28	j)-ψ	j)-ψ	PROPN
ejpam-5208	118	29	-	-	ADJ
ejpam-5208	118	30	generalized	generalize	VERB
ejpam-5208	118	31	semi	semi	ADV
ejpam-5208	118	32	closed	closed	ADJ
ejpam-5208	118	33	(	(	PUNCT
ejpam-5208	118	34	briefly	briefly	ADV
ejpam-5208	118	35	,	,	PUNCT
ejpam-5208	118	36	(	(	PUNCT
ejpam-5208	118	37	i	i	PROPN
ejpam-5208	118	38	,	,	PUNCT
ejpam-5208	118	39	j)ψgs	j)ψgs	PROPN
ejpam-5208	118	40	-	-	PUNCT
ejpam-5208	118	41	closed	closed	ADJ
ejpam-5208	118	42	)	)	PUNCT
ejpam-5208	118	43	function	function	NOUN
ejpam-5208	118	44	if	if	SCONJ
ejpam-5208	118	45	for	for	ADP
ejpam-5208	118	46	every	every	DET
ejpam-5208	118	47	τi	τi	NOUN
ejpam-5208	118	48	-	-	PUNCT
ejpam-5208	118	49	closed	close	VERB
ejpam-5208	118	50	set	set	ADJ
ejpam-5208	118	51	h	h	NOUN
ejpam-5208	118	52	in	in	ADP
ejpam-5208	118	53	x	x	PROPN
ejpam-5208	118	54	,	,	PUNCT
ejpam-5208	118	55	f(h	f(h	PROPN
ejpam-5208	118	56	)	)	PUNCT
ejpam-5208	118	57	is	be	AUX
ejpam-5208	118	58	(	(	PUNCT
ejpam-5208	118	59	i	i	INTJ
ejpam-5208	118	60	,	,	PUNCT
ejpam-5208	118	61	j)-ψgs	j)-ψgs	ADV
ejpam-5208	118	62	-	-	PUNCT
ejpam-5208	118	63	closed	closed	ADJ
ejpam-5208	118	64	set	set	NOUN
ejpam-5208	118	65	in	in	ADP
ejpam-5208	118	66	y	y	PROPN
ejpam-5208	118	67	,	,	PUNCT
ejpam-5208	118	68	where	where	SCONJ
ejpam-5208	118	69	i	i	PRON
ejpam-5208	118	70	∈	∈	PROPN
ejpam-5208	118	71	{	{	PUNCT
ejpam-5208	118	72	1	1	NUM
ejpam-5208	118	73	,	,	PUNCT
ejpam-5208	118	74	2	2	NUM
ejpam-5208	118	75	}	}	PUNCT
ejpam-5208	118	76	.	.	PUNCT
ejpam-5208	119	1	theorem	theorem	NOUN
ejpam-5208	119	2	6	6	NUM
ejpam-5208	119	3	.	.	PUNCT
ejpam-5208	120	1	let	let	VERB
ejpam-5208	120	2	(	(	PUNCT
ejpam-5208	120	3	x	x	NOUN
ejpam-5208	120	4	,	,	PUNCT
ejpam-5208	120	5	τ1	τ1	NOUN
ejpam-5208	120	6	,	,	PUNCT
ejpam-5208	120	7	τ2	τ2	NOUN
ejpam-5208	120	8	)	)	PUNCT
ejpam-5208	120	9	and	and	CCONJ
ejpam-5208	120	10	(	(	PUNCT
ejpam-5208	120	11	y	y	PROPN
ejpam-5208	120	12	,	,	PUNCT
ejpam-5208	120	13	σ1	σ1	PROPN
ejpam-5208	120	14	,	,	PUNCT
ejpam-5208	120	15	σ2	σ2	PROPN
ejpam-5208	120	16	)	)	PUNCT
ejpam-5208	120	17	be	be	VERB
ejpam-5208	120	18	two	two	NUM
ejpam-5208	120	19	bitopological	bitopological	ADJ
ejpam-5208	120	20	spaces	space	NOUN
ejpam-5208	120	21	and	and	CCONJ
ejpam-5208	120	22	h	h	NOUN
ejpam-5208	120	23	⊆	⊆	NUM
ejpam-5208	120	24	x.	x.	NOUN
ejpam-5208	120	25	a	a	DET
ejpam-5208	120	26	function	function	NOUN
ejpam-5208	120	27	f	f	NOUN
ejpam-5208	120	28	:	:	PUNCT
ejpam-5208	120	29	(	(	PUNCT
ejpam-5208	120	30	x	x	NOUN
ejpam-5208	120	31	,	,	PUNCT
ejpam-5208	120	32	τ1	τ1	NOUN
ejpam-5208	120	33	,	,	PUNCT
ejpam-5208	120	34	τ2	τ2	NOUN
ejpam-5208	120	35	)	)	PUNCT
ejpam-5208	120	36	→	→	SYM
ejpam-5208	120	37	(	(	PUNCT
ejpam-5208	120	38	y	y	PROPN
ejpam-5208	120	39	,	,	PUNCT
ejpam-5208	120	40	σ1	σ1	PROPN
ejpam-5208	120	41	,	,	PUNCT
ejpam-5208	120	42	σ2	σ2	PROPN
ejpam-5208	120	43	)	)	PUNCT
ejpam-5208	120	44	is	be	AUX
ejpam-5208	120	45	(	(	PUNCT
ejpam-5208	120	46	i	i	INTJ
ejpam-5208	120	47	,	,	PUNCT
ejpam-5208	120	48	j)-ψgs	j)-ψgs	ADV
ejpam-5208	120	49	-	-	PUNCT
ejpam-5208	120	50	closed	closed	ADJ
ejpam-5208	120	51	function	function	NOUN
ejpam-5208	120	52	if	if	SCONJ
ejpam-5208	120	53	and	and	CCONJ
ejpam-5208	120	54	only	only	ADV
ejpam-5208	120	55	if	if	SCONJ
ejpam-5208	120	56	for	for	ADP
ejpam-5208	120	57	every	every	DET
ejpam-5208	120	58	τi	τi	NOUN
ejpam-5208	120	59	-	-	PUNCT
ejpam-5208	120	60	closed	close	VERB
ejpam-5208	120	61	set	set	ADJ
ejpam-5208	120	62	h	h	NOUN
ejpam-5208	120	63	in	in	ADP
ejpam-5208	120	64	x	x	PROPN
ejpam-5208	120	65	f(cli(h	f(cli(h	NOUN
ejpam-5208	120	66	)	)	PUNCT
ejpam-5208	120	67	)	)	PUNCT
ejpam-5208	121	1	=	=	PUNCT
ejpam-5208	121	2	(	(	PUNCT
ejpam-5208	121	3	i	i	INTJ
ejpam-5208	121	4	,	,	PUNCT
ejpam-5208	121	5	j)-ψgs	j)-ψgs	ADV
ejpam-5208	121	6	-	-	PUNCT
ejpam-5208	121	7	cl(f(h	cl(f(h	NOUN
ejpam-5208	121	8	)	)	PUNCT
ejpam-5208	121	9	)	)	PUNCT
ejpam-5208	121	10	.	.	PUNCT
ejpam-5208	122	1	proof	proof	NOUN
ejpam-5208	122	2	.	.	PUNCT
ejpam-5208	123	1	let	let	VERB
ejpam-5208	123	2	f	f	PRON
ejpam-5208	123	3	be	be	AUX
ejpam-5208	123	4	(	(	PUNCT
ejpam-5208	123	5	i	i	NOUN
ejpam-5208	123	6	,	,	PUNCT
ejpam-5208	123	7	j)-ψgs	j)-ψgs	ADV
ejpam-5208	123	8	-	-	PUNCT
ejpam-5208	123	9	closed	closed	ADJ
ejpam-5208	123	10	function	function	NOUN
ejpam-5208	123	11	.	.	PUNCT
ejpam-5208	124	1	it	it	PRON
ejpam-5208	124	2	follows	follow	VERB
ejpam-5208	124	3	that	that	SCONJ
ejpam-5208	124	4	f(h	f(h	PROPN
ejpam-5208	124	5	)	)	PUNCT
ejpam-5208	124	6	is	be	AUX
ejpam-5208	124	7	(	(	PUNCT
ejpam-5208	124	8	i	i	INTJ
ejpam-5208	124	9	,	,	PUNCT
ejpam-5208	124	10	j)-ψgs	j)-ψgs	ADV
ejpam-5208	124	11	-	-	PUNCT
ejpam-5208	124	12	closed	closed	ADJ
ejpam-5208	124	13	set	set	NOUN
ejpam-5208	124	14	in	in	ADP
ejpam-5208	124	15	y	y	PROPN
ejpam-5208	124	16	for	for	ADP
ejpam-5208	124	17	every	every	DET
ejpam-5208	124	18	τi	τi	NOUN
ejpam-5208	124	19	-	-	PUNCT
ejpam-5208	124	20	closed	close	VERB
ejpam-5208	124	21	set	set	ADJ
ejpam-5208	124	22	h	h	NOUN
ejpam-5208	124	23	in	in	ADP
ejpam-5208	124	24	x.	x.	NOUN
ejpam-5208	124	25	since	since	SCONJ
ejpam-5208	124	26	h	h	PROPN
ejpam-5208	124	27	is	be	AUX
ejpam-5208	124	28	τi	τi	ADV
ejpam-5208	124	29	-	-	PUNCT
ejpam-5208	124	30	closed	closed	ADJ
ejpam-5208	124	31	,	,	PUNCT
ejpam-5208	124	32	cli(h	cli(h	NOUN
ejpam-5208	124	33	)	)	PUNCT
ejpam-5208	124	34	=	=	SYM
ejpam-5208	124	35	h	h	NOUN
ejpam-5208	124	36	,	,	PUNCT
ejpam-5208	124	37	and	and	CCONJ
ejpam-5208	124	38	so	so	ADV
ejpam-5208	124	39	f(cli(h	f(cli(h	PROPN
ejpam-5208	124	40	)	)	PUNCT
ejpam-5208	124	41	)	)	PUNCT
ejpam-5208	125	1	=	=	SYM
ejpam-5208	125	2	f(h	f(h	PROPN
ejpam-5208	125	3	)	)	PUNCT
ejpam-5208	125	4	.	.	PUNCT
ejpam-5208	126	1	also	also	ADV
ejpam-5208	126	2	,	,	PUNCT
ejpam-5208	126	3	since	since	SCONJ
ejpam-5208	126	4	f(h	f(h	PROPN
ejpam-5208	126	5	)	)	PUNCT
ejpam-5208	126	6	is	be	AUX
ejpam-5208	126	7	(	(	PUNCT
ejpam-5208	126	8	i	i	INTJ
ejpam-5208	126	9	,	,	PUNCT
ejpam-5208	126	10	j)-ψgs	j)-ψgs	ADV
ejpam-5208	126	11	-	-	PUNCT
ejpam-5208	126	12	closed	closed	ADJ
ejpam-5208	126	13	set	set	NOUN
ejpam-5208	126	14	,	,	PUNCT
ejpam-5208	126	15	(	(	PUNCT
ejpam-5208	126	16	i	i	INTJ
ejpam-5208	126	17	,	,	PUNCT
ejpam-5208	126	18	j)-ψgs	j)-ψgs	ADV
ejpam-5208	126	19	-	-	PUNCT
ejpam-5208	126	20	cl(f(h	cl(f(h	NOUN
ejpam-5208	126	21	)	)	PUNCT
ejpam-5208	126	22	)	)	PUNCT
ejpam-5208	127	1	=	=	SYM
ejpam-5208	127	2	f(h	f(h	PROPN
ejpam-5208	127	3	)	)	PUNCT
ejpam-5208	127	4	,	,	PUNCT
ejpam-5208	127	5	and	and	CCONJ
ejpam-5208	127	6	hence	hence	ADV
ejpam-5208	127	7	f(cli(h	f(cli(h	NOUN
ejpam-5208	127	8	)	)	PUNCT
ejpam-5208	127	9	)	)	PUNCT
ejpam-5208	128	1	=	=	PUNCT
ejpam-5208	128	2	(	(	PUNCT
ejpam-5208	128	3	i	i	INTJ
ejpam-5208	128	4	,	,	PUNCT
ejpam-5208	128	5	j)-ψgs	j)-ψgs	ADV
ejpam-5208	128	6	-	-	PUNCT
ejpam-5208	128	7	cl(f(h	cl(f(h	NOUN
ejpam-5208	128	8	)	)	PUNCT
ejpam-5208	128	9	)	)	PUNCT
ejpam-5208	128	10	.	.	PUNCT
ejpam-5208	129	1	conversely	conversely	ADV
ejpam-5208	129	2	,	,	PUNCT
ejpam-5208	129	3	suppose	suppose	VERB
ejpam-5208	129	4	f(cli(h	f(cli(h	NOUN
ejpam-5208	129	5	)	)	PUNCT
ejpam-5208	129	6	)	)	PUNCT
ejpam-5208	130	1	=	=	PUNCT
ejpam-5208	130	2	(	(	PUNCT
ejpam-5208	130	3	i	i	INTJ
ejpam-5208	130	4	,	,	PUNCT
ejpam-5208	130	5	j)-ψgs	j)-ψgs	ADV
ejpam-5208	130	6	-	-	PUNCT
ejpam-5208	130	7	cl(f(h	cl(f(h	NOUN
ejpam-5208	130	8	)	)	PUNCT
ejpam-5208	130	9	)	)	PUNCT
ejpam-5208	130	10	for	for	ADP
ejpam-5208	130	11	every	every	DET
ejpam-5208	130	12	τi	τi	NOUN
ejpam-5208	130	13	-	-	PUNCT
ejpam-5208	130	14	closed	close	VERB
ejpam-5208	130	15	set	set	ADJ
ejpam-5208	130	16	h	h	NOUN
ejpam-5208	130	17	in	in	ADP
ejpam-5208	130	18	x.	x.	PROPN
ejpam-5208	130	19	then	then	ADV
ejpam-5208	130	20	cli(h	cli(h	PROPN
ejpam-5208	130	21	)	)	PUNCT
ejpam-5208	130	22	=	=	SYM
ejpam-5208	130	23	h	h	NOUN
ejpam-5208	130	24	,	,	PUNCT
ejpam-5208	130	25	and	and	CCONJ
ejpam-5208	130	26	so	so	ADV
ejpam-5208	130	27	f(cli(h	f(cli(h	PROPN
ejpam-5208	130	28	)	)	PUNCT
ejpam-5208	130	29	)	)	PUNCT
ejpam-5208	131	1	=	=	SYM
ejpam-5208	131	2	f(h	f(h	PROPN
ejpam-5208	131	3	)	)	PUNCT
ejpam-5208	131	4	.	.	PUNCT
ejpam-5208	132	1	it	it	PRON
ejpam-5208	132	2	follows	follow	VERB
ejpam-5208	132	3	that	that	SCONJ
ejpam-5208	132	4	,	,	PUNCT
ejpam-5208	132	5	(	(	PUNCT
ejpam-5208	132	6	i	i	NOUN
ejpam-5208	132	7	,	,	PUNCT
ejpam-5208	132	8	j)-ψgs	j)-ψgs	ADV
ejpam-5208	132	9	-	-	PUNCT
ejpam-5208	132	10	cl(f(h	cl(f(h	NOUN
ejpam-5208	132	11	)	)	PUNCT
ejpam-5208	132	12	)	)	PUNCT
ejpam-5208	133	1	=	=	SYM
ejpam-5208	133	2	f(h).thus	f(h).thu	NOUN
ejpam-5208	133	3	,	,	PUNCT
ejpam-5208	133	4	f(h	f(h	PROPN
ejpam-5208	133	5	)	)	PUNCT
ejpam-5208	133	6	is	be	AUX
ejpam-5208	133	7	(	(	PUNCT
ejpam-5208	133	8	i	i	INTJ
ejpam-5208	133	9	,	,	PUNCT
ejpam-5208	133	10	j)-ψgs	j)-ψgs	ADV
ejpam-5208	133	11	-	-	PUNCT
ejpam-5208	133	12	closed	closed	ADJ
ejpam-5208	133	13	set	set	VERB
ejpam-5208	133	14	by	by	ADP
ejpam-5208	133	15	theorem	theorem	NOUN
ejpam-5208	133	16	2	2	NUM
ejpam-5208	133	17	.	.	PUNCT
ejpam-5208	133	18	consequently	consequently	ADV
ejpam-5208	133	19	,	,	PUNCT
ejpam-5208	133	20	by	by	ADP
ejpam-5208	133	21	definition	definition	NOUN
ejpam-5208	133	22	5	5	NUM
ejpam-5208	133	23	,	,	PUNCT
ejpam-5208	133	24	f	f	PROPN
ejpam-5208	133	25	is	be	AUX
ejpam-5208	133	26	(	(	PUNCT
ejpam-5208	133	27	i	i	NOUN
ejpam-5208	133	28	,	,	PUNCT
ejpam-5208	133	29	j)-ψgs	j)-ψgs	ADV
ejpam-5208	133	30	-	-	PUNCT
ejpam-5208	133	31	closed	closed	ADJ
ejpam-5208	133	32	function	function	NOUN
ejpam-5208	133	33	.	.	PUNCT
ejpam-5208	134	1	theorem	theorem	VERB
ejpam-5208	134	2	7	7	NUM
ejpam-5208	134	3	.	.	PUNCT
ejpam-5208	135	1	let	let	VERB
ejpam-5208	135	2	(	(	PUNCT
ejpam-5208	135	3	x	x	NOUN
ejpam-5208	135	4	,	,	PUNCT
ejpam-5208	135	5	τ1	τ1	NOUN
ejpam-5208	135	6	,	,	PUNCT
ejpam-5208	135	7	τ2	τ2	NOUN
ejpam-5208	135	8	)	)	PUNCT
ejpam-5208	135	9	,	,	PUNCT
ejpam-5208	135	10	(	(	PUNCT
ejpam-5208	135	11	y	y	NOUN
ejpam-5208	135	12	,	,	PUNCT
ejpam-5208	135	13	µ1	µ1	PROPN
ejpam-5208	135	14	,	,	PUNCT
ejpam-5208	135	15	µ2	µ2	PROPN
ejpam-5208	135	16	)	)	PUNCT
ejpam-5208	135	17	,	,	PUNCT
ejpam-5208	135	18	and	and	CCONJ
ejpam-5208	135	19	(	(	PUNCT
ejpam-5208	135	20	z	z	PROPN
ejpam-5208	135	21	,	,	PUNCT
ejpam-5208	135	22	σ1	σ1	PROPN
ejpam-5208	135	23	,	,	PUNCT
ejpam-5208	135	24	σ2	σ2	PROPN
ejpam-5208	135	25	)	)	PUNCT
ejpam-5208	135	26	be	be	VERB
ejpam-5208	135	27	three	three	NUM
ejpam-5208	135	28	bitopological	bitopological	ADJ
ejpam-5208	135	29	spaces	space	NOUN
ejpam-5208	135	30	.	.	PUNCT
ejpam-5208	136	1	if	if	SCONJ
ejpam-5208	136	2	f	f	PROPN
ejpam-5208	136	3	:	:	PUNCT
ejpam-5208	136	4	(	(	PUNCT
ejpam-5208	136	5	x	x	NOUN
ejpam-5208	136	6	,	,	PUNCT
ejpam-5208	136	7	τ1	τ1	NOUN
ejpam-5208	136	8	,	,	PUNCT
ejpam-5208	136	9	τ2	τ2	NOUN
ejpam-5208	136	10	)	)	PUNCT
ejpam-5208	136	11	→	→	SYM
ejpam-5208	136	12	(	(	PUNCT
ejpam-5208	136	13	y	y	PROPN
ejpam-5208	136	14	,	,	PUNCT
ejpam-5208	136	15	µ1	µ1	PROPN
ejpam-5208	136	16	,	,	PUNCT
ejpam-5208	136	17	µ2	µ2	PROPN
ejpam-5208	136	18	)	)	PUNCT
ejpam-5208	136	19	is	be	AUX
ejpam-5208	136	20	τi	τi	ADV
ejpam-5208	136	21	-	-	PUNCT
ejpam-5208	136	22	closed	closed	ADJ
ejpam-5208	136	23	function	function	NOUN
ejpam-5208	136	24	and	and	CCONJ
ejpam-5208	136	25	g	g	NOUN
ejpam-5208	136	26	:	:	PUNCT
ejpam-5208	136	27	(	(	PUNCT
ejpam-5208	136	28	y	y	PROPN
ejpam-5208	136	29	,	,	PUNCT
ejpam-5208	136	30	µ1	µ1	PROPN
ejpam-5208	136	31	,	,	PUNCT
ejpam-5208	136	32	µ2	µ2	PROPN
ejpam-5208	136	33	)	)	PUNCT
ejpam-5208	136	34	→	→	SYM
ejpam-5208	136	35	(	(	PUNCT
ejpam-5208	136	36	z	z	PROPN
ejpam-5208	136	37	,	,	PUNCT
ejpam-5208	136	38	σ1	σ1	PROPN
ejpam-5208	136	39	,	,	PUNCT
ejpam-5208	136	40	σ2	σ2	PROPN
ejpam-5208	136	41	)	)	PUNCT
ejpam-5208	136	42	is	be	AUX
ejpam-5208	136	43	(	(	PUNCT
ejpam-5208	136	44	i	i	X
ejpam-5208	136	45	,	,	PUNCT
ejpam-5208	136	46	j)ψgs	j)ψgs	PROPN
ejpam-5208	136	47	-	-	PUNCT
ejpam-5208	136	48	closed	closed	ADJ
ejpam-5208	136	49	function	function	NOUN
ejpam-5208	136	50	,	,	PUNCT
ejpam-5208	136	51	then	then	ADV
ejpam-5208	136	52	g	g	PROPN
ejpam-5208	136	53	◦	◦	NOUN
ejpam-5208	136	54	f	f	X
ejpam-5208	136	55	:	:	PUNCT
ejpam-5208	136	56	(	(	PUNCT
ejpam-5208	136	57	x	x	NOUN
ejpam-5208	136	58	,	,	PUNCT
ejpam-5208	136	59	τ1	τ1	NOUN
ejpam-5208	136	60	,	,	PUNCT
ejpam-5208	136	61	τ2	τ2	NOUN
ejpam-5208	136	62	)	)	PUNCT
ejpam-5208	136	63	→	→	SYM
ejpam-5208	136	64	(	(	PUNCT
ejpam-5208	136	65	z	z	PROPN
ejpam-5208	136	66	,	,	PUNCT
ejpam-5208	136	67	σ1	σ1	PROPN
ejpam-5208	136	68	,	,	PUNCT
ejpam-5208	136	69	σ2	σ2	PROPN
ejpam-5208	136	70	)	)	PUNCT
ejpam-5208	136	71	is	be	AUX
ejpam-5208	136	72	(	(	PUNCT
ejpam-5208	136	73	i	i	INTJ
ejpam-5208	136	74	,	,	PUNCT
ejpam-5208	136	75	j)-ψgs	j)-ψgs	ADV
ejpam-5208	136	76	-	-	PUNCT
ejpam-5208	136	77	closed	closed	ADJ
ejpam-5208	136	78	function	function	NOUN
ejpam-5208	136	79	.	.	PUNCT
ejpam-5208	137	1	proof	proof	NOUN
ejpam-5208	137	2	.	.	PUNCT
ejpam-5208	138	1	suppose	suppose	VERB
ejpam-5208	138	2	f	f	PRON
ejpam-5208	138	3	be	be	AUX
ejpam-5208	138	4	τi	τi	ADV
ejpam-5208	138	5	-	-	PUNCT
ejpam-5208	138	6	closed	closed	ADJ
ejpam-5208	138	7	function	function	NOUN
ejpam-5208	138	8	.	.	PUNCT
ejpam-5208	139	1	then	then	ADV
ejpam-5208	139	2	f(h	f(h	PROPN
ejpam-5208	139	3	)	)	PUNCT
ejpam-5208	139	4	is	be	AUX
ejpam-5208	139	5	τi	τi	VERB
ejpam-5208	139	6	-	-	PUNCT
ejpam-5208	139	7	closed	closed	ADJ
ejpam-5208	139	8	in	in	ADP
ejpam-5208	139	9	y	y	PROPN
ejpam-5208	139	10	for	for	ADP
ejpam-5208	139	11	every	every	DET
ejpam-5208	139	12	τi	τi	NOUN
ejpam-5208	139	13	-	-	PUNCT
ejpam-5208	139	14	closed	close	VERB
ejpam-5208	139	15	set	set	ADJ
ejpam-5208	139	16	h	h	NOUN
ejpam-5208	139	17	in	in	ADP
ejpam-5208	139	18	x.	x.	NOUN
ejpam-5208	139	19	since	since	SCONJ
ejpam-5208	139	20	g	g	PROPN
ejpam-5208	139	21	is	be	AUX
ejpam-5208	139	22	(	(	PUNCT
ejpam-5208	139	23	i	i	PROPN
ejpam-5208	139	24	,	,	PUNCT
ejpam-5208	139	25	j)-ψgs	j)-ψgs	ADV
ejpam-5208	139	26	-	-	PUNCT
ejpam-5208	139	27	closed	closed	ADJ
ejpam-5208	139	28	function	function	NOUN
ejpam-5208	139	29	,	,	PUNCT
ejpam-5208	139	30	g(f(h	g(f(h	PROPN
ejpam-5208	139	31	)	)	PUNCT
ejpam-5208	139	32	)	)	PUNCT
ejpam-5208	140	1	is	be	AUX
ejpam-5208	140	2	(	(	PUNCT
ejpam-5208	140	3	i	i	INTJ
ejpam-5208	140	4	,	,	PUNCT
ejpam-5208	140	5	j)-ψgs	j)-ψgs	ADV
ejpam-5208	140	6	-	-	PUNCT
ejpam-5208	140	7	closed	closed	ADJ
ejpam-5208	140	8	set	set	NOUN
ejpam-5208	140	9	in	in	ADP
ejpam-5208	140	10	z.	z.	PROPN
ejpam-5208	140	11	hence	hence	ADV
ejpam-5208	140	12	g	g	PROPN
ejpam-5208	140	13	◦	◦	PROPN
ejpam-5208	140	14	f	f	X
ejpam-5208	140	15	is	be	AUX
ejpam-5208	140	16	(	(	PUNCT
ejpam-5208	140	17	i	i	NOUN
ejpam-5208	140	18	,	,	PUNCT
ejpam-5208	140	19	j)-ψgs	j)-ψgs	ADV
ejpam-5208	140	20	-	-	PUNCT
ejpam-5208	140	21	closed	closed	ADJ
ejpam-5208	140	22	function	function	NOUN
ejpam-5208	140	23	.	.	PUNCT
ejpam-5208	141	1	5	5	X
ejpam-5208	141	2	.	.	X
ejpam-5208	141	3	ψgs	ψgs	ADV
ejpam-5208	141	4	-	-	PUNCT
ejpam-5208	141	5	continuous	continuous	ADJ
ejpam-5208	141	6	function	function	NOUN
ejpam-5208	141	7	in	in	ADP
ejpam-5208	141	8	bts	bt	NOUN
ejpam-5208	141	9	in	in	ADP
ejpam-5208	141	10	this	this	DET
ejpam-5208	141	11	section	section	NOUN
ejpam-5208	141	12	ψgs	ψgs	ADV
ejpam-5208	141	13	-	-	PUNCT
ejpam-5208	141	14	continuous	continuous	ADJ
ejpam-5208	141	15	function	function	NOUN
ejpam-5208	141	16	is	be	AUX
ejpam-5208	141	17	defined	define	VERB
ejpam-5208	141	18	in	in	ADP
ejpam-5208	141	19	bts	bt	NOUN
ejpam-5208	141	20	and	and	CCONJ
ejpam-5208	141	21	some	some	PRON
ejpam-5208	141	22	of	of	ADP
ejpam-5208	141	23	its	its	PRON
ejpam-5208	141	24	properties	property	NOUN
ejpam-5208	141	25	are	be	AUX
ejpam-5208	141	26	established	establish	VERB
ejpam-5208	141	27	.	.	PUNCT
ejpam-5208	142	1	moreover	moreover	ADV
ejpam-5208	142	2	,	,	PUNCT
ejpam-5208	142	3	equivalent	equivalent	ADJ
ejpam-5208	142	4	statements	statement	NOUN
ejpam-5208	142	5	involving	involve	VERB
ejpam-5208	142	6	ψgs	ψgs	ADV
ejpam-5208	142	7	-	-	PUNCT
ejpam-5208	142	8	continuous	continuous	ADJ
ejpam-5208	142	9	function	function	NOUN
ejpam-5208	142	10	,	,	PUNCT
ejpam-5208	142	11	ψgsopen	ψgsopen	NOUN
ejpam-5208	142	12	,	,	PUNCT
ejpam-5208	142	13	and	and	CCONJ
ejpam-5208	142	14	ψgs	ψgs	ADV
ejpam-5208	142	15	-	-	PUNCT
ejpam-5208	142	16	closed	close	VERB
ejpam-5208	142	17	functions	function	NOUN
ejpam-5208	142	18	are	be	AUX
ejpam-5208	142	19	provided	provide	VERB
ejpam-5208	142	20	.	.	PUNCT
ejpam-5208	143	1	l.	l.	PROPN
ejpam-5208	143	2	m.	m.	PROPN
ejpam-5208	143	3	tutanes	tutane	NOUN
ejpam-5208	143	4	/	/	SYM
ejpam-5208	143	5	eur	eur	PROPN
ejpam-5208	143	6	.	.	PUNCT
ejpam-5208	144	1	j.	j.	PROPN
ejpam-5208	144	2	pure	pure	PROPN
ejpam-5208	144	3	appl	appl	PROPN
ejpam-5208	144	4	.	.	PROPN
ejpam-5208	144	5	math	math	PROPN
ejpam-5208	144	6	,	,	PUNCT
ejpam-5208	144	7	17	17	NUM
ejpam-5208	144	8	(	(	PUNCT
ejpam-5208	144	9	3	3	NUM
ejpam-5208	144	10	)	)	PUNCT
ejpam-5208	144	11	(	(	PUNCT
ejpam-5208	144	12	2024	2024	NUM
ejpam-5208	144	13	)	)	PUNCT
ejpam-5208	144	14	,	,	PUNCT
ejpam-5208	144	15	2173	2173	NUM
ejpam-5208	144	16	-	-	SYM
ejpam-5208	144	17	2181	2181	NUM
ejpam-5208	144	18	2178	2178	NUM
ejpam-5208	144	19	definition	definition	NOUN
ejpam-5208	144	20	6	6	NUM
ejpam-5208	144	21	.	.	PUNCT
ejpam-5208	145	1	let	let	VERB
ejpam-5208	145	2	(	(	PUNCT
ejpam-5208	145	3	x	x	NOUN
ejpam-5208	145	4	,	,	PUNCT
ejpam-5208	145	5	τ1	τ1	NOUN
ejpam-5208	145	6	,	,	PUNCT
ejpam-5208	145	7	τ2	τ2	NOUN
ejpam-5208	145	8	)	)	PUNCT
ejpam-5208	145	9	and	and	CCONJ
ejpam-5208	145	10	(	(	PUNCT
ejpam-5208	145	11	y	y	PROPN
ejpam-5208	145	12	,	,	PUNCT
ejpam-5208	145	13	σ1	σ1	PROPN
ejpam-5208	145	14	,	,	PUNCT
ejpam-5208	145	15	σ2	σ2	PROPN
ejpam-5208	145	16	)	)	PUNCT
ejpam-5208	145	17	be	be	VERB
ejpam-5208	145	18	two	two	NUM
ejpam-5208	145	19	bitopological	bitopological	ADJ
ejpam-5208	145	20	spaces	space	NOUN
ejpam-5208	145	21	.	.	PUNCT
ejpam-5208	146	1	a	a	DET
ejpam-5208	146	2	function	function	NOUN
ejpam-5208	146	3	f	f	NOUN
ejpam-5208	146	4	:	:	PUNCT
ejpam-5208	146	5	(	(	PUNCT
ejpam-5208	146	6	x	x	NOUN
ejpam-5208	146	7	,	,	PUNCT
ejpam-5208	146	8	τ1	τ1	NOUN
ejpam-5208	146	9	,	,	PUNCT
ejpam-5208	146	10	τ2	τ2	NOUN
ejpam-5208	146	11	)	)	PUNCT
ejpam-5208	146	12	→	→	SYM
ejpam-5208	146	13	(	(	PUNCT
ejpam-5208	146	14	y	y	PROPN
ejpam-5208	146	15	,	,	PUNCT
ejpam-5208	146	16	σ1	σ1	PROPN
ejpam-5208	146	17	,	,	PUNCT
ejpam-5208	146	18	σ2	σ2	PROPN
ejpam-5208	146	19	)	)	PUNCT
ejpam-5208	146	20	is	be	AUX
ejpam-5208	146	21	said	say	VERB
ejpam-5208	146	22	to	to	PART
ejpam-5208	146	23	be	be	AUX
ejpam-5208	146	24	an	an	DET
ejpam-5208	146	25	(	(	PUNCT
ejpam-5208	146	26	i	i	NOUN
ejpam-5208	146	27	,	,	PUNCT
ejpam-5208	146	28	j)-ψ	j)-ψ	PROPN
ejpam-5208	146	29	generalized	generalize	VERB
ejpam-5208	146	30	semi	semi	ADV
ejpam-5208	146	31	continuous	continuous	ADJ
ejpam-5208	146	32	(	(	PUNCT
ejpam-5208	146	33	briefly	briefly	ADV
ejpam-5208	146	34	,	,	PUNCT
ejpam-5208	146	35	(	(	PUNCT
ejpam-5208	146	36	i	i	NOUN
ejpam-5208	146	37	,	,	PUNCT
ejpam-5208	146	38	j)-ψgs	j)-ψgs	ADV
ejpam-5208	146	39	-	-	ADJ
ejpam-5208	146	40	continuous	continuous	ADJ
ejpam-5208	146	41	)	)	PUNCT
ejpam-5208	146	42	function	function	NOUN
ejpam-5208	146	43	if	if	SCONJ
ejpam-5208	146	44	the	the	DET
ejpam-5208	146	45	inverse	inverse	ADJ
ejpam-5208	146	46	image	image	NOUN
ejpam-5208	146	47	of	of	ADP
ejpam-5208	146	48	each	each	DET
ejpam-5208	146	49	σi	σi	NOUN
ejpam-5208	146	50	-	-	PUNCT
ejpam-5208	146	51	closed	closed	ADJ
ejpam-5208	146	52	set	set	NOUN
ejpam-5208	146	53	in	in	ADP
ejpam-5208	146	54	y	y	PROPN
ejpam-5208	146	55	is	be	AUX
ejpam-5208	146	56	(	(	PUNCT
ejpam-5208	146	57	i	i	PROPN
ejpam-5208	146	58	,	,	PUNCT
ejpam-5208	146	59	j)-ψgsclosed	j)-ψgsclose	VERB
ejpam-5208	146	60	set	set	VERB
ejpam-5208	146	61	in	in	ADP
ejpam-5208	146	62	x	x	NOUN
ejpam-5208	146	63	,	,	PUNCT
ejpam-5208	146	64	where	where	SCONJ
ejpam-5208	146	65	i	i	PRON
ejpam-5208	146	66	∈	∈	PROPN
ejpam-5208	146	67	{	{	PUNCT
ejpam-5208	146	68	1	1	NUM
ejpam-5208	146	69	,	,	PUNCT
ejpam-5208	146	70	2	2	NUM
ejpam-5208	146	71	}	}	PUNCT
ejpam-5208	146	72	.	.	PUNCT
ejpam-5208	147	1	theorem	theorem	ADJ
ejpam-5208	147	2	8	8	NUM
ejpam-5208	147	3	.	.	PUNCT
ejpam-5208	148	1	let	let	VERB
ejpam-5208	148	2	(	(	PUNCT
ejpam-5208	148	3	x	x	NOUN
ejpam-5208	148	4	,	,	PUNCT
ejpam-5208	148	5	τ1	τ1	NOUN
ejpam-5208	148	6	,	,	PUNCT
ejpam-5208	148	7	τ2	τ2	NOUN
ejpam-5208	148	8	)	)	PUNCT
ejpam-5208	148	9	and	and	CCONJ
ejpam-5208	148	10	(	(	PUNCT
ejpam-5208	148	11	y	y	PROPN
ejpam-5208	148	12	,	,	PUNCT
ejpam-5208	148	13	σ1	σ1	PROPN
ejpam-5208	148	14	,	,	PUNCT
ejpam-5208	148	15	σ2	σ2	PROPN
ejpam-5208	148	16	)	)	PUNCT
ejpam-5208	148	17	be	be	VERB
ejpam-5208	148	18	two	two	NUM
ejpam-5208	148	19	bitopological	bitopological	ADJ
ejpam-5208	148	20	spaces	space	NOUN
ejpam-5208	148	21	and	and	CCONJ
ejpam-5208	148	22	a	a	DET
ejpam-5208	148	23	⊆	⊆	NUM
ejpam-5208	148	24	x.	x.	NOUN
ejpam-5208	148	25	if	if	SCONJ
ejpam-5208	148	26	a	a	DET
ejpam-5208	148	27	function	function	NOUN
ejpam-5208	148	28	f	f	X
ejpam-5208	148	29	:	:	PUNCT
ejpam-5208	148	30	(	(	PUNCT
ejpam-5208	148	31	x	x	NOUN
ejpam-5208	148	32	,	,	PUNCT
ejpam-5208	148	33	τ1	τ1	NOUN
ejpam-5208	148	34	,	,	PUNCT
ejpam-5208	148	35	τ2	τ2	NOUN
ejpam-5208	148	36	)	)	PUNCT
ejpam-5208	148	37	→	→	SYM
ejpam-5208	148	38	(	(	PUNCT
ejpam-5208	148	39	y	y	PROPN
ejpam-5208	148	40	,	,	PUNCT
ejpam-5208	148	41	σ1	σ1	PROPN
ejpam-5208	148	42	,	,	PUNCT
ejpam-5208	148	43	σ2	σ2	PROPN
ejpam-5208	148	44	)	)	PUNCT
ejpam-5208	148	45	is	be	AUX
ejpam-5208	148	46	(	(	PUNCT
ejpam-5208	148	47	i	i	NOUN
ejpam-5208	148	48	,	,	PUNCT
ejpam-5208	148	49	j)-ψgs	j)-ψgs	ADV
ejpam-5208	148	50	-	-	ADJ
ejpam-5208	148	51	continuous	continuous	ADJ
ejpam-5208	148	52	,	,	PUNCT
ejpam-5208	148	53	then	then	ADV
ejpam-5208	148	54	f((i	f((i	NOUN
ejpam-5208	148	55	,	,	PUNCT
ejpam-5208	148	56	j)-ψgs	j)-ψgs	ADV
ejpam-5208	148	57	-	-	PUNCT
ejpam-5208	148	58	cl(a	cl(a	NUM
ejpam-5208	148	59	)	)	PUNCT
ejpam-5208	148	60	)	)	PUNCT
ejpam-5208	149	1	⊆	⊆	NUM
ejpam-5208	149	2	cli(f(a	cli(f(a	NOUN
ejpam-5208	149	3	)	)	PUNCT
ejpam-5208	149	4	)	)	PUNCT
ejpam-5208	149	5	.	.	PUNCT
ejpam-5208	150	1	proof	proof	NOUN
ejpam-5208	150	2	.	.	PUNCT
ejpam-5208	151	1	let	let	VERB
ejpam-5208	151	2	f	f	PRON
ejpam-5208	151	3	be	be	AUX
ejpam-5208	151	4	(	(	PUNCT
ejpam-5208	151	5	i	i	NOUN
ejpam-5208	151	6	,	,	PUNCT
ejpam-5208	151	7	j)-ψgs	j)-ψgs	ADV
ejpam-5208	151	8	-	-	ADJ
ejpam-5208	151	9	continuous	continuous	ADJ
ejpam-5208	151	10	function	function	NOUN
ejpam-5208	151	11	and	and	CCONJ
ejpam-5208	151	12	a	a	DET
ejpam-5208	151	13	⊆	⊆	NUM
ejpam-5208	151	14	x.	x.	NOUN
ejpam-5208	151	15	then	then	ADV
ejpam-5208	151	16	f(a	f(a	PROPN
ejpam-5208	151	17	)	)	PUNCT
ejpam-5208	152	1	⊆	⊆	NUM
ejpam-5208	152	2	y	y	PROPN
ejpam-5208	152	3	.	.	PUNCT
ejpam-5208	153	1	note	note	VERB
ejpam-5208	153	2	that	that	SCONJ
ejpam-5208	153	3	f(a	f(a	NOUN
ejpam-5208	153	4	)	)	PUNCT
ejpam-5208	153	5	⊆	⊆	NUM
ejpam-5208	153	6	cli(f(a	cli(f(a	NOUN
ejpam-5208	153	7	)	)	PUNCT
ejpam-5208	153	8	)	)	PUNCT
ejpam-5208	153	9	,	,	PUNCT
ejpam-5208	153	10	and	and	CCONJ
ejpam-5208	153	11	so	so	ADV
ejpam-5208	153	12	a	a	DET
ejpam-5208	153	13	⊆	⊆	NUM
ejpam-5208	153	14	f−1(cli(f(a	f−1(cli(f(a	NOUN
ejpam-5208	153	15	)	)	PUNCT
ejpam-5208	153	16	)	)	PUNCT
ejpam-5208	153	17	)	)	PUNCT
ejpam-5208	153	18	.	.	PUNCT
ejpam-5208	154	1	also	also	ADV
ejpam-5208	154	2	,	,	PUNCT
ejpam-5208	154	3	note	note	VERB
ejpam-5208	154	4	that	that	DET
ejpam-5208	154	5	cli(f(a	cli(f(a	NOUN
ejpam-5208	154	6	)	)	PUNCT
ejpam-5208	154	7	)	)	PUNCT
ejpam-5208	154	8	is	be	AUX
ejpam-5208	154	9	σi	σi	NOUN
ejpam-5208	154	10	-	-	PUNCT
ejpam-5208	154	11	closed	closed	ADJ
ejpam-5208	154	12	in	in	ADP
ejpam-5208	154	13	y	y	PROPN
ejpam-5208	154	14	,	,	PUNCT
ejpam-5208	154	15	and	and	CCONJ
ejpam-5208	154	16	so	so	ADV
ejpam-5208	154	17	f−1(cli(f(a	f−1(cli(f(a	PUNCT
ejpam-5208	154	18	)	)	PUNCT
ejpam-5208	154	19	)	)	PUNCT
ejpam-5208	154	20	)	)	PUNCT
ejpam-5208	155	1	is	be	AUX
ejpam-5208	155	2	(	(	PUNCT
ejpam-5208	155	3	i	i	INTJ
ejpam-5208	155	4	,	,	PUNCT
ejpam-5208	155	5	j)-ψgs	j)-ψgs	ADV
ejpam-5208	155	6	-	-	PUNCT
ejpam-5208	155	7	closed	closed	ADJ
ejpam-5208	155	8	set	set	NOUN
ejpam-5208	155	9	in	in	ADP
ejpam-5208	155	10	x.	x.	NOUN
ejpam-5208	155	11	since	since	SCONJ
ejpam-5208	155	12	a	a	DET
ejpam-5208	155	13	⊆	⊆	NUM
ejpam-5208	155	14	f−1(cli(f(a	f−1(cli(f(a	NOUN
ejpam-5208	155	15	)	)	PUNCT
ejpam-5208	155	16	)	)	PUNCT
ejpam-5208	155	17	)	)	PUNCT
ejpam-5208	155	18	and	and	CCONJ
ejpam-5208	155	19	f−1(cli(f(a	f−1(cli(f(a	PUNCT
ejpam-5208	155	20	)	)	PUNCT
ejpam-5208	155	21	)	)	PUNCT
ejpam-5208	155	22	)	)	PUNCT
ejpam-5208	156	1	is	be	AUX
ejpam-5208	156	2	(	(	PUNCT
ejpam-5208	156	3	i	i	INTJ
ejpam-5208	156	4	,	,	PUNCT
ejpam-5208	156	5	j)-ψgs	j)-ψgs	ADV
ejpam-5208	156	6	-	-	PUNCT
ejpam-5208	156	7	closed	closed	ADJ
ejpam-5208	156	8	set	set	NOUN
ejpam-5208	156	9	,	,	PUNCT
ejpam-5208	156	10	(	(	PUNCT
ejpam-5208	156	11	i	i	INTJ
ejpam-5208	156	12	,	,	PUNCT
ejpam-5208	156	13	j)-ψgs	j)-ψgs	ADV
ejpam-5208	156	14	-	-	PUNCT
ejpam-5208	156	15	cl(a	cl(a	NUM
ejpam-5208	156	16	)	)	PUNCT
ejpam-5208	156	17	⊆	⊆	NUM
ejpam-5208	156	18	f−1(cli(f(a	f−1(cli(f(a	NOUN
ejpam-5208	156	19	)	)	PUNCT
ejpam-5208	156	20	)	)	PUNCT
ejpam-5208	156	21	)	)	PUNCT
ejpam-5208	156	22	,	,	PUNCT
ejpam-5208	156	23	by	by	ADP
ejpam-5208	156	24	remark	remark	NOUN
ejpam-5208	156	25	2(iii	2(iii	NUM
ejpam-5208	156	26	)	)	PUNCT
ejpam-5208	156	27	.	.	PUNCT
ejpam-5208	157	1	thus	thus	ADV
ejpam-5208	157	2	,	,	PUNCT
ejpam-5208	157	3	f((i	f((i	NOUN
ejpam-5208	157	4	,	,	PUNCT
ejpam-5208	157	5	j)-ψgs	j)-ψgs	ADV
ejpam-5208	157	6	-	-	PUNCT
ejpam-5208	157	7	cl(a	cl(a	NUM
ejpam-5208	157	8	)	)	PUNCT
ejpam-5208	157	9	)	)	PUNCT
ejpam-5208	157	10	⊆	⊆	NUM
ejpam-5208	157	11	cli(f(a	cli(f(a	NOUN
ejpam-5208	157	12	)	)	PUNCT
ejpam-5208	157	13	)	)	PUNCT
ejpam-5208	157	14	.	.	PUNCT
ejpam-5208	158	1	theorem	theorem	VERB
ejpam-5208	158	2	9	9	NUM
ejpam-5208	158	3	.	.	PUNCT
ejpam-5208	159	1	a	a	DET
ejpam-5208	159	2	function	function	NOUN
ejpam-5208	159	3	f	f	NOUN
ejpam-5208	159	4	:	:	PUNCT
ejpam-5208	159	5	(	(	PUNCT
ejpam-5208	159	6	x	x	NOUN
ejpam-5208	159	7	,	,	PUNCT
ejpam-5208	159	8	τ1	τ1	NOUN
ejpam-5208	159	9	,	,	PUNCT
ejpam-5208	159	10	τ2	τ2	NOUN
ejpam-5208	159	11	)	)	PUNCT
ejpam-5208	159	12	→	→	SYM
ejpam-5208	159	13	(	(	PUNCT
ejpam-5208	159	14	y	y	PROPN
ejpam-5208	159	15	,	,	PUNCT
ejpam-5208	159	16	µ1	µ1	PROPN
ejpam-5208	159	17	,	,	PUNCT
ejpam-5208	159	18	µ2	µ2	PROPN
ejpam-5208	159	19	)	)	PUNCT
ejpam-5208	159	20	is	be	AUX
ejpam-5208	159	21	(	(	PUNCT
ejpam-5208	159	22	i	i	INTJ
ejpam-5208	159	23	,	,	PUNCT
ejpam-5208	159	24	j)-ψgs	j)-ψgs	ADV
ejpam-5208	159	25	-	-	ADJ
ejpam-5208	159	26	continuous	continuous	ADJ
ejpam-5208	159	27	in	in	ADP
ejpam-5208	159	28	bts	bt	NOUN
ejpam-5208	159	29	if	if	SCONJ
ejpam-5208	159	30	and	and	CCONJ
ejpam-5208	159	31	only	only	ADV
ejpam-5208	159	32	if	if	SCONJ
ejpam-5208	159	33	the	the	DET
ejpam-5208	159	34	inverse	inverse	ADJ
ejpam-5208	159	35	image	image	NOUN
ejpam-5208	159	36	of	of	ADP
ejpam-5208	159	37	every	every	DET
ejpam-5208	159	38	µi	µi	PROPN
ejpam-5208	159	39	-	-	PUNCT
ejpam-5208	159	40	open	open	ADJ
ejpam-5208	159	41	set	set	NOUN
ejpam-5208	159	42	in	in	ADP
ejpam-5208	159	43	y	y	PROPN
ejpam-5208	159	44	is	be	AUX
ejpam-5208	159	45	a	a	DET
ejpam-5208	159	46	(	(	PUNCT
ejpam-5208	159	47	i	i	NOUN
ejpam-5208	159	48	,	,	PUNCT
ejpam-5208	159	49	j)-ψgs	j)-ψgs	ADV
ejpam-5208	159	50	-	-	ADJ
ejpam-5208	159	51	open	open	ADJ
ejpam-5208	159	52	set	set	NOUN
ejpam-5208	159	53	in	in	ADP
ejpam-5208	159	54	x.	x.	NOUN
ejpam-5208	159	55	proof	proof	NOUN
ejpam-5208	159	56	.	.	PUNCT
ejpam-5208	160	1	let	let	VERB
ejpam-5208	160	2	f	f	PRON
ejpam-5208	160	3	be	be	AUX
ejpam-5208	160	4	(	(	PUNCT
ejpam-5208	160	5	i	i	NOUN
ejpam-5208	160	6	,	,	PUNCT
ejpam-5208	160	7	j)-ψgs	j)-ψgs	ADV
ejpam-5208	160	8	-	-	ADJ
ejpam-5208	160	9	continuous	continuous	ADJ
ejpam-5208	160	10	function	function	NOUN
ejpam-5208	160	11	and	and	CCONJ
ejpam-5208	160	12	g	g	NOUN
ejpam-5208	160	13	be	be	AUX
ejpam-5208	160	14	µi	µi	ADV
ejpam-5208	160	15	-	-	PUNCT
ejpam-5208	160	16	open	open	ADJ
ejpam-5208	160	17	set	set	NOUN
ejpam-5208	160	18	in	in	ADP
ejpam-5208	160	19	y	y	PROPN
ejpam-5208	160	20	.	.	PUNCT
ejpam-5208	161	1	then	then	ADV
ejpam-5208	161	2	y∖g	y∖g	PROPN
ejpam-5208	161	3	is	be	AUX
ejpam-5208	161	4	µi	µi	ADV
ejpam-5208	161	5	-	-	PUNCT
ejpam-5208	161	6	closed	close	VERB
ejpam-5208	161	7	set	set	NOUN
ejpam-5208	161	8	in	in	ADP
ejpam-5208	161	9	y	y	PROPN
ejpam-5208	161	10	.	.	PUNCT
ejpam-5208	162	1	by	by	ADP
ejpam-5208	162	2	assumption	assumption	NOUN
ejpam-5208	162	3	,	,	PUNCT
ejpam-5208	162	4	f−1(y	f−1(y	PROPN
ejpam-5208	162	5	∖g	∖g	PROPN
ejpam-5208	162	6	)	)	PUNCT
ejpam-5208	162	7	=	=	SYM
ejpam-5208	163	1	x∖f−1(g	x∖f−1(g	X
ejpam-5208	163	2	)	)	PUNCT
ejpam-5208	163	3	is	be	AUX
ejpam-5208	163	4	(	(	PUNCT
ejpam-5208	163	5	i	i	INTJ
ejpam-5208	163	6	,	,	PUNCT
ejpam-5208	163	7	j)-ψgs	j)-ψgs	ADV
ejpam-5208	163	8	-	-	PUNCT
ejpam-5208	163	9	closed	closed	ADJ
ejpam-5208	163	10	set	set	NOUN
ejpam-5208	163	11	in	in	ADP
ejpam-5208	163	12	x.	x.	NOUN
ejpam-5208	163	13	hence	hence	ADV
ejpam-5208	163	14	,	,	PUNCT
ejpam-5208	163	15	f−1(g	f−1(g	PROPN
ejpam-5208	163	16	)	)	PUNCT
ejpam-5208	163	17	is	be	AUX
ejpam-5208	163	18	(	(	PUNCT
ejpam-5208	163	19	i	i	INTJ
ejpam-5208	163	20	,	,	PUNCT
ejpam-5208	163	21	j)-ψgs	j)-ψgs	ADV
ejpam-5208	163	22	-	-	ADJ
ejpam-5208	163	23	open	open	ADJ
ejpam-5208	163	24	set	set	NOUN
ejpam-5208	163	25	in	in	ADP
ejpam-5208	163	26	x.	x.	NOUN
ejpam-5208	163	27	conversely	conversely	ADV
ejpam-5208	163	28	,	,	PUNCT
ejpam-5208	163	29	let	let	VERB
ejpam-5208	163	30	b	b	X
ejpam-5208	163	31	be	be	AUX
ejpam-5208	163	32	µi	µi	ADV
ejpam-5208	163	33	-	-	PUNCT
ejpam-5208	163	34	open	open	ADJ
ejpam-5208	163	35	set	set	NOUN
ejpam-5208	163	36	in	in	ADP
ejpam-5208	163	37	y	y	PROPN
ejpam-5208	163	38	such	such	ADJ
ejpam-5208	163	39	that	that	DET
ejpam-5208	163	40	f−1(b	f−1(b	PROPN
ejpam-5208	163	41	)	)	PUNCT
ejpam-5208	163	42	is	be	AUX
ejpam-5208	163	43	(	(	PUNCT
ejpam-5208	163	44	i	i	INTJ
ejpam-5208	163	45	,	,	PUNCT
ejpam-5208	163	46	j)-ψgs	j)-ψgs	ADV
ejpam-5208	163	47	-	-	ADJ
ejpam-5208	163	48	open	open	ADJ
ejpam-5208	163	49	set	set	NOUN
ejpam-5208	163	50	in	in	ADP
ejpam-5208	163	51	x.	x.	PROPN
ejpam-5208	163	52	then	then	ADV
ejpam-5208	163	53	x∖f−1(b	x∖f−1(b	NUM
ejpam-5208	163	54	)	)	PUNCT
ejpam-5208	163	55	=	=	SYM
ejpam-5208	164	1	f−1(y∖b	f−1(y∖b	PROPN
ejpam-5208	164	2	)	)	PUNCT
ejpam-5208	164	3	is	be	AUX
ejpam-5208	164	4	(	(	PUNCT
ejpam-5208	164	5	i	i	INTJ
ejpam-5208	164	6	,	,	PUNCT
ejpam-5208	164	7	j)-ψgs	j)-ψgs	ADV
ejpam-5208	164	8	-	-	PUNCT
ejpam-5208	164	9	closed	closed	ADJ
ejpam-5208	164	10	set	set	NOUN
ejpam-5208	164	11	in	in	ADP
ejpam-5208	164	12	x	x	PUNCT
ejpam-5208	164	13	for	for	SCONJ
ejpam-5208	164	14	every	every	DET
ejpam-5208	164	15	µi	µi	ADV
ejpam-5208	164	16	-	-	PUNCT
ejpam-5208	164	17	closed	close	VERB
ejpam-5208	164	18	set	set	NOUN
ejpam-5208	164	19	y	y	PROPN
ejpam-5208	164	20	∖b	∖b	VERB
ejpam-5208	164	21	in	in	ADP
ejpam-5208	164	22	y	y	PROPN
ejpam-5208	164	23	.	.	PUNCT
ejpam-5208	165	1	hence	hence	ADV
ejpam-5208	165	2	f	f	PROPN
ejpam-5208	165	3	is	be	AUX
ejpam-5208	165	4	(	(	PUNCT
ejpam-5208	165	5	i	i	NOUN
ejpam-5208	165	6	,	,	PUNCT
ejpam-5208	165	7	j)-ψgs	j)-ψgs	ADV
ejpam-5208	165	8	-	-	ADJ
ejpam-5208	165	9	continuous	continuous	ADJ
ejpam-5208	165	10	function	function	NOUN
ejpam-5208	165	11	.	.	PUNCT
ejpam-5208	166	1	theorem	theorem	ADJ
ejpam-5208	166	2	10	10	NUM
ejpam-5208	166	3	.	.	PUNCT
ejpam-5208	167	1	let	let	VERB
ejpam-5208	167	2	(	(	PUNCT
ejpam-5208	167	3	x	x	NOUN
ejpam-5208	167	4	,	,	PUNCT
ejpam-5208	167	5	τ1	τ1	NOUN
ejpam-5208	167	6	,	,	PUNCT
ejpam-5208	167	7	τ2	τ2	NOUN
ejpam-5208	167	8	)	)	PUNCT
ejpam-5208	167	9	and	and	CCONJ
ejpam-5208	167	10	(	(	PUNCT
ejpam-5208	167	11	y	y	PROPN
ejpam-5208	167	12	,	,	PUNCT
ejpam-5208	167	13	σ1	σ1	PROPN
ejpam-5208	167	14	,	,	PUNCT
ejpam-5208	167	15	σ2	σ2	PROPN
ejpam-5208	167	16	)	)	PUNCT
ejpam-5208	167	17	be	be	VERB
ejpam-5208	167	18	two	two	NUM
ejpam-5208	167	19	bitopological	bitopological	ADJ
ejpam-5208	167	20	spaces	space	NOUN
ejpam-5208	167	21	and	and	CCONJ
ejpam-5208	167	22	a	a	DET
ejpam-5208	167	23	⊆	⊆	NUM
ejpam-5208	167	24	x.	x.	NOUN
ejpam-5208	167	25	if	if	SCONJ
ejpam-5208	167	26	a	a	DET
ejpam-5208	167	27	function	function	NOUN
ejpam-5208	167	28	f	f	X
ejpam-5208	167	29	:	:	PUNCT
ejpam-5208	167	30	(	(	PUNCT
ejpam-5208	167	31	x	x	NOUN
ejpam-5208	167	32	,	,	PUNCT
ejpam-5208	167	33	τ1	τ1	NOUN
ejpam-5208	167	34	,	,	PUNCT
ejpam-5208	167	35	τ2	τ2	NOUN
ejpam-5208	167	36	)	)	PUNCT
ejpam-5208	167	37	→	→	SYM
ejpam-5208	167	38	(	(	PUNCT
ejpam-5208	167	39	y	y	PROPN
ejpam-5208	167	40	,	,	PUNCT
ejpam-5208	167	41	σ1	σ1	PROPN
ejpam-5208	167	42	,	,	PUNCT
ejpam-5208	167	43	σ2	σ2	PROPN
ejpam-5208	167	44	)	)	PUNCT
ejpam-5208	167	45	is	be	AUX
ejpam-5208	167	46	(	(	PUNCT
ejpam-5208	167	47	i	i	NOUN
ejpam-5208	167	48	,	,	PUNCT
ejpam-5208	167	49	j)-ψgs	j)-ψgs	ADV
ejpam-5208	167	50	-	-	ADJ
ejpam-5208	167	51	continuous	continuous	ADJ
ejpam-5208	167	52	,	,	PUNCT
ejpam-5208	167	53	then	then	ADV
ejpam-5208	167	54	inti(f(b	inti(f(b	NOUN
ejpam-5208	167	55	)	)	PUNCT
ejpam-5208	167	56	)	)	PUNCT
ejpam-5208	168	1	⊆	⊆	NUM
ejpam-5208	168	2	f((i	f((i	NOUN
ejpam-5208	168	3	,	,	PUNCT
ejpam-5208	168	4	j)-ψgs	j)-ψgs	ADV
ejpam-5208	168	5	-	-	PUNCT
ejpam-5208	168	6	int(b	int(b	NOUN
ejpam-5208	168	7	)	)	PUNCT
ejpam-5208	168	8	)	)	PUNCT
ejpam-5208	168	9	.	.	PUNCT
ejpam-5208	169	1	proof	proof	NOUN
ejpam-5208	169	2	.	.	PUNCT
ejpam-5208	170	1	let	let	VERB
ejpam-5208	170	2	f	f	PRON
ejpam-5208	170	3	be	be	AUX
ejpam-5208	170	4	(	(	PUNCT
ejpam-5208	170	5	i	i	NOUN
ejpam-5208	170	6	,	,	PUNCT
ejpam-5208	170	7	j)-ψgs	j)-ψgs	ADV
ejpam-5208	170	8	-	-	ADJ
ejpam-5208	170	9	continuous	continuous	ADJ
ejpam-5208	170	10	function	function	NOUN
ejpam-5208	170	11	and	and	CCONJ
ejpam-5208	170	12	b	b	NOUN
ejpam-5208	170	13	⊆	⊆	NUM
ejpam-5208	170	14	x.	x.	NOUN
ejpam-5208	170	15	then	then	ADV
ejpam-5208	170	16	f(b	f(b	PROPN
ejpam-5208	170	17	)	)	PUNCT
ejpam-5208	171	1	⊆	⊆	NUM
ejpam-5208	171	2	y	y	NOUN
ejpam-5208	171	3	.	.	PUNCT
ejpam-5208	172	1	now	now	ADV
ejpam-5208	172	2	,	,	PUNCT
ejpam-5208	172	3	inti(f(b	inti(f(b	PROPN
ejpam-5208	172	4	)	)	PUNCT
ejpam-5208	172	5	)	)	PUNCT
ejpam-5208	173	1	⊆	⊆	NUM
ejpam-5208	173	2	f(b	f(b	NOUN
ejpam-5208	173	3	)	)	PUNCT
ejpam-5208	173	4	,	,	PUNCT
ejpam-5208	173	5	and	and	CCONJ
ejpam-5208	173	6	so	so	ADV
ejpam-5208	173	7	f−1(inti(f(b	f−1(inti(f(b	NOUN
ejpam-5208	173	8	)	)	PUNCT
ejpam-5208	173	9	)	)	PUNCT
ejpam-5208	173	10	)	)	PUNCT
ejpam-5208	174	1	⊆	⊆	NUM
ejpam-5208	174	2	b.	b.	PROPN
ejpam-5208	174	3	note	note	NOUN
ejpam-5208	174	4	that	that	SCONJ
ejpam-5208	174	5	inti(f(b	inti(f(b	PROPN
ejpam-5208	174	6	)	)	PUNCT
ejpam-5208	174	7	)	)	PUNCT
ejpam-5208	174	8	is	be	AUX
ejpam-5208	174	9	σi	σi	NOUN
ejpam-5208	174	10	-	-	PUNCT
ejpam-5208	174	11	open	open	ADJ
ejpam-5208	174	12	in	in	ADP
ejpam-5208	174	13	y	y	PROPN
ejpam-5208	174	14	,	,	PUNCT
ejpam-5208	174	15	and	and	CCONJ
ejpam-5208	174	16	so	so	ADV
ejpam-5208	174	17	f−1(inti(f(b	f−1(inti(f(b	NOUN
ejpam-5208	174	18	)	)	PUNCT
ejpam-5208	174	19	)	)	PUNCT
ejpam-5208	174	20	)	)	PUNCT
ejpam-5208	175	1	is	be	AUX
ejpam-5208	175	2	(	(	PUNCT
ejpam-5208	175	3	i	i	INTJ
ejpam-5208	175	4	,	,	PUNCT
ejpam-5208	175	5	j)-ψgs	j)-ψgs	ADV
ejpam-5208	175	6	-	-	ADJ
ejpam-5208	175	7	open	open	ADJ
ejpam-5208	175	8	set	set	NOUN
ejpam-5208	175	9	in	in	ADP
ejpam-5208	175	10	x	x	PUNCT
ejpam-5208	175	11	by	by	ADP
ejpam-5208	175	12	theorem	theorem	NOUN
ejpam-5208	175	13	9	9	NUM
ejpam-5208	175	14	.	.	PUNCT
ejpam-5208	175	15	since	since	SCONJ
ejpam-5208	175	16	f−1(inti(f(b	f−1(inti(f(b	NOUN
ejpam-5208	175	17	)	)	PUNCT
ejpam-5208	175	18	)	)	PUNCT
ejpam-5208	175	19	)	)	PUNCT
ejpam-5208	176	1	⊆	⊆	NUM
ejpam-5208	176	2	b	b	NOUN
ejpam-5208	176	3	and	and	CCONJ
ejpam-5208	176	4	f−1(inti(f(b	f−1(inti(f(b	NOUN
ejpam-5208	176	5	)	)	PUNCT
ejpam-5208	176	6	)	)	PUNCT
ejpam-5208	176	7	)	)	PUNCT
ejpam-5208	176	8	is	be	AUX
ejpam-5208	176	9	(	(	PUNCT
ejpam-5208	176	10	i	i	INTJ
ejpam-5208	176	11	,	,	PUNCT
ejpam-5208	176	12	j)-ψgs	j)-ψgs	ADV
ejpam-5208	176	13	-	-	PUNCT
ejpam-5208	176	14	open	open	ADJ
ejpam-5208	176	15	set	set	NOUN
ejpam-5208	176	16	,	,	PUNCT
ejpam-5208	176	17	f−1(inti(f(b	f−1(inti(f(b	NOUN
ejpam-5208	176	18	)	)	PUNCT
ejpam-5208	176	19	)	)	PUNCT
ejpam-5208	176	20	)	)	PUNCT
ejpam-5208	177	1	⊆	⊆	X
ejpam-5208	177	2	(	(	PUNCT
ejpam-5208	177	3	i	i	NOUN
ejpam-5208	177	4	,	,	PUNCT
ejpam-5208	177	5	j)-ψgs	j)-ψgs	ADV
ejpam-5208	177	6	-	-	PUNCT
ejpam-5208	177	7	int(b	int(b	NOUN
ejpam-5208	177	8	)	)	PUNCT
ejpam-5208	177	9	by	by	ADP
ejpam-5208	177	10	remark	remark	NOUN
ejpam-5208	177	11	1(iii	1(iii	NUM
ejpam-5208	177	12	)	)	PUNCT
ejpam-5208	177	13	.	.	PUNCT
ejpam-5208	178	1	thus	thus	ADV
ejpam-5208	178	2	,	,	PUNCT
ejpam-5208	178	3	inti(f(b	inti(f(b	NOUN
ejpam-5208	178	4	)	)	PUNCT
ejpam-5208	178	5	)	)	PUNCT
ejpam-5208	178	6	⊆	⊆	NUM
ejpam-5208	178	7	f((i	f((i	NOUN
ejpam-5208	178	8	,	,	PUNCT
ejpam-5208	178	9	j)-ψgs	j)-ψgs	ADV
ejpam-5208	178	10	-	-	PUNCT
ejpam-5208	178	11	int(b	int(b	NOUN
ejpam-5208	178	12	)	)	PUNCT
ejpam-5208	178	13	)	)	PUNCT
ejpam-5208	178	14	.	.	PUNCT
ejpam-5208	179	1	theorem	theorem	VERB
ejpam-5208	179	2	11	11	NUM
ejpam-5208	179	3	.	.	PUNCT
ejpam-5208	180	1	let	let	VERB
ejpam-5208	180	2	(	(	PUNCT
ejpam-5208	180	3	x	x	NOUN
ejpam-5208	180	4	,	,	PUNCT
ejpam-5208	180	5	τ1	τ1	NOUN
ejpam-5208	180	6	,	,	PUNCT
ejpam-5208	180	7	τ2	τ2	NOUN
ejpam-5208	180	8	)	)	PUNCT
ejpam-5208	180	9	and	and	CCONJ
ejpam-5208	180	10	(	(	PUNCT
ejpam-5208	180	11	y	y	PROPN
ejpam-5208	180	12	,	,	PUNCT
ejpam-5208	180	13	σ1	σ1	PROPN
ejpam-5208	180	14	,	,	PUNCT
ejpam-5208	180	15	σ2	σ2	PROPN
ejpam-5208	180	16	)	)	PUNCT
ejpam-5208	180	17	be	be	VERB
ejpam-5208	180	18	two	two	NUM
ejpam-5208	180	19	bitopological	bitopological	ADJ
ejpam-5208	180	20	spaces	space	NOUN
ejpam-5208	180	21	.	.	PUNCT
ejpam-5208	181	1	then	then	ADV
ejpam-5208	181	2	the	the	DET
ejpam-5208	181	3	following	follow	VERB
ejpam-5208	181	4	statements	statement	NOUN
ejpam-5208	181	5	are	be	AUX
ejpam-5208	181	6	equivalent	equivalent	ADJ
ejpam-5208	181	7	.	.	PUNCT
ejpam-5208	182	1	(	(	PUNCT
ejpam-5208	182	2	i	i	NOUN
ejpam-5208	182	3	)	)	PUNCT
ejpam-5208	182	4	f	f	NOUN
ejpam-5208	182	5	:	:	PUNCT
ejpam-5208	182	6	(	(	PUNCT
ejpam-5208	182	7	x	x	NOUN
ejpam-5208	182	8	,	,	PUNCT
ejpam-5208	182	9	τ1	τ1	NOUN
ejpam-5208	182	10	,	,	PUNCT
ejpam-5208	182	11	τ2	τ2	NOUN
ejpam-5208	182	12	)	)	PUNCT
ejpam-5208	182	13	→	→	SYM
ejpam-5208	182	14	(	(	PUNCT
ejpam-5208	182	15	y	y	PROPN
ejpam-5208	182	16	,	,	PUNCT
ejpam-5208	182	17	σ1	σ1	PROPN
ejpam-5208	182	18	,	,	PUNCT
ejpam-5208	182	19	σ2	σ2	PROPN
ejpam-5208	182	20	)	)	PUNCT
ejpam-5208	182	21	is	be	AUX
ejpam-5208	182	22	(	(	PUNCT
ejpam-5208	182	23	i	i	INTJ
ejpam-5208	182	24	,	,	PUNCT
ejpam-5208	182	25	j)-ψgs	j)-ψgs	ADV
ejpam-5208	182	26	-	-	ADJ
ejpam-5208	182	27	continuous	continuous	ADJ
ejpam-5208	182	28	function	function	NOUN
ejpam-5208	182	29	;	;	PUNCT
ejpam-5208	182	30	(	(	PUNCT
ejpam-5208	182	31	ii	ii	X
ejpam-5208	182	32	)	)	PUNCT
ejpam-5208	182	33	f−1	f−1	PROPN
ejpam-5208	182	34	is	be	AUX
ejpam-5208	182	35	(	(	PUNCT
ejpam-5208	182	36	i	i	NOUN
ejpam-5208	182	37	,	,	PUNCT
ejpam-5208	182	38	j)-ψgs	j)-ψgs	ADV
ejpam-5208	182	39	-	-	PUNCT
ejpam-5208	182	40	open	open	ADJ
ejpam-5208	182	41	function	function	NOUN
ejpam-5208	182	42	;	;	PUNCT
ejpam-5208	182	43	and	and	CCONJ
ejpam-5208	182	44	l.	l.	PROPN
ejpam-5208	182	45	m.	m.	PROPN
ejpam-5208	182	46	tutanes	tutane	NOUN
ejpam-5208	182	47	/	/	SYM
ejpam-5208	182	48	eur	eur	PROPN
ejpam-5208	182	49	.	.	PUNCT
ejpam-5208	183	1	j.	j.	PROPN
ejpam-5208	183	2	pure	pure	PROPN
ejpam-5208	183	3	appl	appl	PROPN
ejpam-5208	183	4	.	.	PROPN
ejpam-5208	183	5	math	math	PROPN
ejpam-5208	183	6	,	,	PUNCT
ejpam-5208	183	7	17	17	NUM
ejpam-5208	183	8	(	(	PUNCT
ejpam-5208	183	9	3	3	NUM
ejpam-5208	183	10	)	)	PUNCT
ejpam-5208	183	11	(	(	PUNCT
ejpam-5208	183	12	2024	2024	NUM
ejpam-5208	183	13	)	)	PUNCT
ejpam-5208	183	14	,	,	PUNCT
ejpam-5208	183	15	2173	2173	NUM
ejpam-5208	183	16	-	-	SYM
ejpam-5208	183	17	2181	2181	NUM
ejpam-5208	183	18	2179	2179	NUM
ejpam-5208	183	19	(	(	PUNCT
ejpam-5208	183	20	iii	iii	X
ejpam-5208	183	21	)	)	PUNCT
ejpam-5208	183	22	f−1	f−1	PROPN
ejpam-5208	183	23	is	be	AUX
ejpam-5208	183	24	(	(	PUNCT
ejpam-5208	183	25	i	i	INTJ
ejpam-5208	183	26	,	,	PUNCT
ejpam-5208	183	27	j)-ψgs	j)-ψgs	ADV
ejpam-5208	183	28	-	-	PUNCT
ejpam-5208	183	29	closed	closed	ADJ
ejpam-5208	183	30	function	function	NOUN
ejpam-5208	183	31	.	.	PUNCT
ejpam-5208	184	1	proof	proof	NOUN
ejpam-5208	184	2	.	.	PUNCT
ejpam-5208	185	1	(	(	PUNCT
ejpam-5208	185	2	i	i	NOUN
ejpam-5208	185	3	)	)	PUNCT
ejpam-5208	186	1	=	=	NOUN
ejpam-5208	186	2	⇒	⇒	NOUN
ejpam-5208	186	3	(	(	PUNCT
ejpam-5208	186	4	ii	ii	NOUN
ejpam-5208	186	5	):	):	PUNCT
ejpam-5208	186	6	let	let	VERB
ejpam-5208	186	7	f	f	PRON
ejpam-5208	186	8	be	be	AUX
ejpam-5208	186	9	(	(	PUNCT
ejpam-5208	186	10	i	i	NOUN
ejpam-5208	186	11	,	,	PUNCT
ejpam-5208	186	12	j)-ψgs	j)-ψgs	ADV
ejpam-5208	186	13	-	-	ADJ
ejpam-5208	186	14	continuous	continuous	ADJ
ejpam-5208	186	15	function	function	NOUN
ejpam-5208	186	16	.	.	PUNCT
ejpam-5208	187	1	we	we	PRON
ejpam-5208	187	2	want	want	VERB
ejpam-5208	187	3	to	to	PART
ejpam-5208	187	4	show	show	VERB
ejpam-5208	187	5	that	that	SCONJ
ejpam-5208	187	6	f−1	f−1	PROPN
ejpam-5208	187	7	:	:	PUNCT
ejpam-5208	187	8	(	(	PUNCT
ejpam-5208	187	9	y	y	PROPN
ejpam-5208	187	10	,	,	PUNCT
ejpam-5208	187	11	σ1	σ1	PROPN
ejpam-5208	187	12	,	,	PUNCT
ejpam-5208	187	13	σ2	σ2	NOUN
ejpam-5208	187	14	)	)	PUNCT
ejpam-5208	187	15	→	→	SYM
ejpam-5208	187	16	(	(	PUNCT
ejpam-5208	187	17	x	x	NOUN
ejpam-5208	187	18	,	,	PUNCT
ejpam-5208	187	19	τ1	τ1	NOUN
ejpam-5208	187	20	,	,	PUNCT
ejpam-5208	187	21	τ2	τ2	NOUN
ejpam-5208	187	22	)	)	PUNCT
ejpam-5208	187	23	is	be	AUX
ejpam-5208	187	24	(	(	PUNCT
ejpam-5208	187	25	i	i	NOUN
ejpam-5208	187	26	,	,	PUNCT
ejpam-5208	187	27	j)-ψgs	j)-ψgs	ADV
ejpam-5208	187	28	-	-	PUNCT
ejpam-5208	187	29	open	open	ADJ
ejpam-5208	187	30	function	function	NOUN
ejpam-5208	187	31	.	.	PUNCT
ejpam-5208	188	1	now	now	ADV
ejpam-5208	188	2	,	,	PUNCT
ejpam-5208	188	3	let	let	VERB
ejpam-5208	188	4	a	a	PRON
ejpam-5208	188	5	be	be	AUX
ejpam-5208	188	6	σi	σi	NOUN
ejpam-5208	188	7	-	-	ADJ
ejpam-5208	188	8	open	open	ADJ
ejpam-5208	188	9	set	set	NOUN
ejpam-5208	188	10	in	in	ADP
ejpam-5208	188	11	y	y	PROPN
ejpam-5208	188	12	.	.	PUNCT
ejpam-5208	189	1	since	since	SCONJ
ejpam-5208	189	2	f	f	PROPN
ejpam-5208	189	3	is	be	AUX
ejpam-5208	189	4	(	(	PUNCT
ejpam-5208	189	5	i	i	NOUN
ejpam-5208	189	6	,	,	PUNCT
ejpam-5208	189	7	j)-ψgs	j)-ψgs	ADV
ejpam-5208	189	8	-	-	ADJ
ejpam-5208	189	9	continuous	continuous	ADJ
ejpam-5208	189	10	function	function	NOUN
ejpam-5208	189	11	,	,	PUNCT
ejpam-5208	189	12	by	by	ADP
ejpam-5208	189	13	theorem	theorem	NOUN
ejpam-5208	189	14	9	9	NUM
ejpam-5208	189	15	,	,	PUNCT
ejpam-5208	189	16	f−1(a	f−1(a	NOUN
ejpam-5208	189	17	)	)	PUNCT
ejpam-5208	189	18	is	be	AUX
ejpam-5208	189	19	(	(	PUNCT
ejpam-5208	189	20	i	i	PRON
ejpam-5208	189	21	,	,	PUNCT
ejpam-5208	189	22	j)-ψgsopen	j)-ψgsopen	PUNCT
ejpam-5208	189	23	set	set	VERB
ejpam-5208	189	24	in	in	ADP
ejpam-5208	189	25	x.	x.	NOUN
ejpam-5208	189	26	hence	hence	ADV
ejpam-5208	189	27	f−1	f−1	PROPN
ejpam-5208	189	28	is	be	AUX
ejpam-5208	189	29	(	(	PUNCT
ejpam-5208	189	30	i	i	INTJ
ejpam-5208	189	31	,	,	PUNCT
ejpam-5208	189	32	j)-ψgs	j)-ψgs	ADV
ejpam-5208	189	33	-	-	PUNCT
ejpam-5208	189	34	open	open	ADJ
ejpam-5208	189	35	function	function	NOUN
ejpam-5208	189	36	.	.	PUNCT
ejpam-5208	190	1	(	(	PUNCT
ejpam-5208	190	2	ii	ii	NOUN
ejpam-5208	190	3	)	)	PUNCT
ejpam-5208	190	4	=	=	NOUN
ejpam-5208	190	5	⇒	⇒	NOUN
ejpam-5208	190	6	(	(	PUNCT
ejpam-5208	190	7	iii	iii	NOUN
ejpam-5208	190	8	):	):	PUNCT
ejpam-5208	190	9	suppose	suppose	VERB
ejpam-5208	190	10	f−1	f−1	PROPN
ejpam-5208	190	11	is	be	AUX
ejpam-5208	190	12	(	(	PUNCT
ejpam-5208	190	13	i	i	NOUN
ejpam-5208	190	14	,	,	PUNCT
ejpam-5208	190	15	j)-ψgs	j)-ψgs	ADV
ejpam-5208	190	16	-	-	PUNCT
ejpam-5208	190	17	open	open	ADJ
ejpam-5208	190	18	function	function	NOUN
ejpam-5208	190	19	and	and	CCONJ
ejpam-5208	190	20	b	b	PROPN
ejpam-5208	190	21	a	a	DET
ejpam-5208	190	22	σi	σi	NOUN
ejpam-5208	190	23	-	-	PUNCT
ejpam-5208	190	24	closed	closed	ADJ
ejpam-5208	190	25	in	in	ADP
ejpam-5208	190	26	y	y	PROPN
ejpam-5208	190	27	.	.	PUNCT
ejpam-5208	191	1	then	then	ADV
ejpam-5208	191	2	y	y	PROPN
ejpam-5208	191	3	∖b	∖b	PROPN
ejpam-5208	191	4	is	be	AUX
ejpam-5208	191	5	σi	σi	NOUN
ejpam-5208	191	6	-	-	PUNCT
ejpam-5208	191	7	open	open	ADJ
ejpam-5208	191	8	in	in	ADP
ejpam-5208	191	9	y	y	PROPN
ejpam-5208	191	10	,	,	PUNCT
ejpam-5208	191	11	and	and	CCONJ
ejpam-5208	191	12	so	so	ADV
ejpam-5208	191	13	x∖f−1(b	x∖f−1(b	X
ejpam-5208	191	14	)	)	PUNCT
ejpam-5208	191	15	=	=	SYM
ejpam-5208	191	16	f−1(y	f−1(y	PROPN
ejpam-5208	191	17	∖b	∖b	PROPN
ejpam-5208	191	18	)	)	PUNCT
ejpam-5208	191	19	is	be	AUX
ejpam-5208	191	20	(	(	PUNCT
ejpam-5208	191	21	i	i	NOUN
ejpam-5208	191	22	,	,	PUNCT
ejpam-5208	191	23	j)-ψgs	j)-ψgs	ADV
ejpam-5208	191	24	-	-	ADJ
ejpam-5208	191	25	open	open	ADJ
ejpam-5208	191	26	set	set	NOUN
ejpam-5208	191	27	in	in	ADP
ejpam-5208	191	28	x	x	PUNCT
ejpam-5208	191	29	since	since	SCONJ
ejpam-5208	191	30	f−1	f−1	PROPN
ejpam-5208	191	31	is	be	AUX
ejpam-5208	191	32	(	(	PUNCT
ejpam-5208	191	33	i	i	INTJ
ejpam-5208	191	34	,	,	PUNCT
ejpam-5208	191	35	j)-ψgs	j)-ψgs	ADV
ejpam-5208	191	36	-	-	PUNCT
ejpam-5208	191	37	open	open	ADJ
ejpam-5208	191	38	function	function	NOUN
ejpam-5208	191	39	.	.	PUNCT
ejpam-5208	192	1	it	it	PRON
ejpam-5208	192	2	follows	follow	VERB
ejpam-5208	192	3	that	that	SCONJ
ejpam-5208	192	4	f−1(b	f−1(b	PROPN
ejpam-5208	192	5	)	)	PUNCT
ejpam-5208	192	6	is	be	AUX
ejpam-5208	192	7	(	(	PUNCT
ejpam-5208	192	8	i	i	INTJ
ejpam-5208	192	9	,	,	PUNCT
ejpam-5208	192	10	j)-ψgs	j)-ψgs	ADV
ejpam-5208	192	11	-	-	PUNCT
ejpam-5208	192	12	closed	closed	ADJ
ejpam-5208	192	13	set	set	NOUN
ejpam-5208	192	14	in	in	ADP
ejpam-5208	192	15	x	x	NOUN
ejpam-5208	192	16	,	,	PUNCT
ejpam-5208	192	17	and	and	CCONJ
ejpam-5208	192	18	thus	thus	ADV
ejpam-5208	192	19	f−1	f−1	PROPN
ejpam-5208	192	20	is	be	AUX
ejpam-5208	192	21	(	(	PUNCT
ejpam-5208	192	22	i	i	INTJ
ejpam-5208	192	23	,	,	PUNCT
ejpam-5208	192	24	j)-ψgs	j)-ψgs	ADV
ejpam-5208	192	25	-	-	PUNCT
ejpam-5208	192	26	closed	closed	ADJ
ejpam-5208	192	27	function	function	NOUN
ejpam-5208	192	28	.	.	PUNCT
ejpam-5208	193	1	(	(	PUNCT
ejpam-5208	193	2	iii	iii	X
ejpam-5208	193	3	)	)	PUNCT
ejpam-5208	193	4	=	=	NOUN
ejpam-5208	193	5	⇒	⇒	NOUN
ejpam-5208	193	6	(	(	PUNCT
ejpam-5208	193	7	i	i	NOUN
ejpam-5208	193	8	):	):	PUNCT
ejpam-5208	193	9	assume	assume	VERB
ejpam-5208	193	10	f−1	f−1	PROPN
ejpam-5208	193	11	is	be	AUX
ejpam-5208	193	12	(	(	PUNCT
ejpam-5208	193	13	i	i	INTJ
ejpam-5208	193	14	,	,	PUNCT
ejpam-5208	193	15	j)-ψgs	j)-ψgs	ADV
ejpam-5208	193	16	-	-	PUNCT
ejpam-5208	193	17	closed	closed	ADJ
ejpam-5208	193	18	function	function	NOUN
ejpam-5208	193	19	and	and	CCONJ
ejpam-5208	193	20	c	c	AUX
ejpam-5208	193	21	be	be	AUX
ejpam-5208	193	22	σi	σi	NOUN
ejpam-5208	193	23	-	-	PUNCT
ejpam-5208	193	24	closed	close	VERB
ejpam-5208	193	25	set	set	NOUN
ejpam-5208	193	26	in	in	ADP
ejpam-5208	193	27	y	y	PROPN
ejpam-5208	193	28	.	.	PUNCT
ejpam-5208	194	1	then	then	ADV
ejpam-5208	194	2	,	,	PUNCT
ejpam-5208	194	3	by	by	ADP
ejpam-5208	194	4	assumption	assumption	NOUN
ejpam-5208	194	5	,	,	PUNCT
ejpam-5208	194	6	f−1(c	f−1(c	PROPN
ejpam-5208	194	7	)	)	PUNCT
ejpam-5208	194	8	is	be	AUX
ejpam-5208	194	9	(	(	PUNCT
ejpam-5208	194	10	i	i	INTJ
ejpam-5208	194	11	,	,	PUNCT
ejpam-5208	194	12	j)-ψgs	j)-ψgs	ADV
ejpam-5208	194	13	-	-	PUNCT
ejpam-5208	194	14	closed	closed	ADJ
ejpam-5208	194	15	set	set	NOUN
ejpam-5208	194	16	in	in	ADP
ejpam-5208	194	17	x.	x.	NOUN
ejpam-5208	194	18	thus	thus	ADV
ejpam-5208	194	19	,	,	PUNCT
ejpam-5208	194	20	by	by	ADP
ejpam-5208	194	21	definition	definition	NOUN
ejpam-5208	194	22	6	6	NUM
ejpam-5208	194	23	,	,	PUNCT
ejpam-5208	194	24	f	f	PROPN
ejpam-5208	194	25	is	be	AUX
ejpam-5208	194	26	(	(	PUNCT
ejpam-5208	194	27	i	i	NOUN
ejpam-5208	194	28	,	,	PUNCT
ejpam-5208	194	29	j)-ψgs	j)-ψgs	ADV
ejpam-5208	194	30	-	-	ADJ
ejpam-5208	194	31	continuous	continuous	ADJ
ejpam-5208	194	32	function	function	NOUN
ejpam-5208	194	33	.	.	PUNCT
ejpam-5208	195	1	6	6	X
ejpam-5208	195	2	.	.	X
ejpam-5208	195	3	ψgs	ψgs	ADV
ejpam-5208	195	4	-	-	PUNCT
ejpam-5208	195	5	irresolute	irresolute	ADJ
ejpam-5208	195	6	function	function	NOUN
ejpam-5208	195	7	in	in	ADP
ejpam-5208	195	8	bts	bt	NOUN
ejpam-5208	195	9	in	in	ADP
ejpam-5208	195	10	this	this	DET
ejpam-5208	195	11	section	section	NOUN
ejpam-5208	195	12	,	,	PUNCT
ejpam-5208	195	13	the	the	DET
ejpam-5208	195	14	ψgs	ψgs	ADV
ejpam-5208	195	15	-	-	PUNCT
ejpam-5208	195	16	irresolute	irresolute	ADJ
ejpam-5208	195	17	function	function	NOUN
ejpam-5208	195	18	is	be	AUX
ejpam-5208	195	19	introduced	introduce	VERB
ejpam-5208	195	20	and	and	CCONJ
ejpam-5208	195	21	defined	define	VERB
ejpam-5208	195	22	within	within	ADP
ejpam-5208	195	23	bts	bt	NOUN
ejpam-5208	195	24	,	,	PUNCT
ejpam-5208	195	25	with	with	ADP
ejpam-5208	195	26	several	several	ADJ
ejpam-5208	195	27	of	of	ADP
ejpam-5208	195	28	its	its	PRON
ejpam-5208	195	29	properties	property	NOUN
ejpam-5208	195	30	established	establish	VERB
ejpam-5208	195	31	.	.	PUNCT
ejpam-5208	196	1	furthermore	furthermore	ADV
ejpam-5208	196	2	,	,	PUNCT
ejpam-5208	196	3	a	a	DET
ejpam-5208	196	4	characterization	characterization	NOUN
ejpam-5208	196	5	of	of	ADP
ejpam-5208	196	6	the	the	DET
ejpam-5208	196	7	ψgs	ψgs	ADV
ejpam-5208	196	8	-	-	PUNCT
ejpam-5208	196	9	irresolute	irresolute	ADJ
ejpam-5208	196	10	function	function	NOUN
ejpam-5208	196	11	is	be	AUX
ejpam-5208	196	12	presented	present	VERB
ejpam-5208	196	13	.	.	PUNCT
ejpam-5208	197	1	definition	definition	NOUN
ejpam-5208	197	2	7	7	NUM
ejpam-5208	197	3	.	.	PUNCT
ejpam-5208	198	1	let	let	VERB
ejpam-5208	198	2	(	(	PUNCT
ejpam-5208	198	3	x	x	NOUN
ejpam-5208	198	4	,	,	PUNCT
ejpam-5208	198	5	τ1	τ1	NOUN
ejpam-5208	198	6	,	,	PUNCT
ejpam-5208	198	7	τ2	τ2	NOUN
ejpam-5208	198	8	)	)	PUNCT
ejpam-5208	198	9	and	and	CCONJ
ejpam-5208	198	10	(	(	PUNCT
ejpam-5208	198	11	y	y	PROPN
ejpam-5208	198	12	,	,	PUNCT
ejpam-5208	198	13	σ1	σ1	PROPN
ejpam-5208	198	14	,	,	PUNCT
ejpam-5208	198	15	σ2	σ2	PROPN
ejpam-5208	198	16	)	)	PUNCT
ejpam-5208	198	17	be	be	VERB
ejpam-5208	198	18	two	two	NUM
ejpam-5208	198	19	bitopological	bitopological	ADJ
ejpam-5208	198	20	spaces	space	NOUN
ejpam-5208	198	21	.	.	PUNCT
ejpam-5208	199	1	a	a	DET
ejpam-5208	199	2	function	function	NOUN
ejpam-5208	199	3	f	f	NOUN
ejpam-5208	199	4	:	:	PUNCT
ejpam-5208	199	5	(	(	PUNCT
ejpam-5208	199	6	x	x	NOUN
ejpam-5208	199	7	,	,	PUNCT
ejpam-5208	199	8	τ1	τ1	NOUN
ejpam-5208	199	9	,	,	PUNCT
ejpam-5208	199	10	τ2	τ2	NOUN
ejpam-5208	199	11	)	)	PUNCT
ejpam-5208	199	12	→	→	SYM
ejpam-5208	199	13	(	(	PUNCT
ejpam-5208	199	14	y	y	PROPN
ejpam-5208	199	15	,	,	PUNCT
ejpam-5208	199	16	σ1	σ1	PROPN
ejpam-5208	199	17	,	,	PUNCT
ejpam-5208	199	18	σ2	σ2	PROPN
ejpam-5208	199	19	)	)	PUNCT
ejpam-5208	199	20	is	be	AUX
ejpam-5208	199	21	said	say	VERB
ejpam-5208	199	22	to	to	PART
ejpam-5208	199	23	be	be	AUX
ejpam-5208	199	24	(	(	PUNCT
ejpam-5208	199	25	i	i	PROPN
ejpam-5208	199	26	,	,	PUNCT
ejpam-5208	199	27	j)-ψ	j)-ψ	PROPN
ejpam-5208	199	28	generalized	generalize	VERB
ejpam-5208	199	29	semi	semi	ADJ
ejpam-5208	199	30	irresolute	irresolute	ADJ
ejpam-5208	199	31	(	(	PUNCT
ejpam-5208	199	32	briefly	briefly	ADV
ejpam-5208	199	33	,	,	PUNCT
ejpam-5208	199	34	(	(	PUNCT
ejpam-5208	199	35	i	i	X
ejpam-5208	199	36	,	,	PUNCT
ejpam-5208	199	37	j)ψgs	j)ψgs	PROPN
ejpam-5208	199	38	-	-	PUNCT
ejpam-5208	199	39	irresolute	irresolute	NOUN
ejpam-5208	199	40	)	)	PUNCT
ejpam-5208	199	41	function	function	NOUN
ejpam-5208	199	42	if	if	SCONJ
ejpam-5208	199	43	the	the	DET
ejpam-5208	199	44	inverse	inverse	ADJ
ejpam-5208	199	45	image	image	NOUN
ejpam-5208	199	46	of	of	ADP
ejpam-5208	199	47	each	each	DET
ejpam-5208	199	48	(	(	PUNCT
ejpam-5208	199	49	i	i	PROPN
ejpam-5208	199	50	,	,	PUNCT
ejpam-5208	199	51	j)-ψgs	j)-ψgs	ADV
ejpam-5208	199	52	-	-	PUNCT
ejpam-5208	199	53	closed	closed	ADJ
ejpam-5208	199	54	set	set	NOUN
ejpam-5208	199	55	in	in	ADP
ejpam-5208	199	56	y	y	PROPN
ejpam-5208	199	57	is	be	AUX
ejpam-5208	199	58	(	(	PUNCT
ejpam-5208	199	59	i	i	PROPN
ejpam-5208	199	60	,	,	PUNCT
ejpam-5208	199	61	j)-ψgsclosed	j)-ψgsclose	VERB
ejpam-5208	199	62	set	set	VERB
ejpam-5208	199	63	in	in	ADP
ejpam-5208	199	64	x	x	NOUN
ejpam-5208	199	65	,	,	PUNCT
ejpam-5208	199	66	where	where	SCONJ
ejpam-5208	199	67	i	i	PRON
ejpam-5208	199	68	∈	∈	PROPN
ejpam-5208	199	69	{	{	PUNCT
ejpam-5208	199	70	1	1	NUM
ejpam-5208	199	71	,	,	PUNCT
ejpam-5208	199	72	2	2	NUM
ejpam-5208	199	73	}	}	PUNCT
ejpam-5208	199	74	.	.	PUNCT
ejpam-5208	200	1	theorem	theorem	NOUN
ejpam-5208	200	2	12	12	NUM
ejpam-5208	200	3	.	.	PUNCT
ejpam-5208	201	1	a	a	DET
ejpam-5208	201	2	function	function	NOUN
ejpam-5208	201	3	f	f	NOUN
ejpam-5208	201	4	:	:	PUNCT
ejpam-5208	201	5	(	(	PUNCT
ejpam-5208	201	6	x	x	NOUN
ejpam-5208	201	7	,	,	PUNCT
ejpam-5208	201	8	τ1	τ1	NOUN
ejpam-5208	201	9	,	,	PUNCT
ejpam-5208	201	10	τ2	τ2	NOUN
ejpam-5208	201	11	)	)	PUNCT
ejpam-5208	201	12	→	→	SYM
ejpam-5208	201	13	(	(	PUNCT
ejpam-5208	201	14	y	y	PROPN
ejpam-5208	201	15	,	,	PUNCT
ejpam-5208	201	16	σ1	σ1	PROPN
ejpam-5208	201	17	,	,	PUNCT
ejpam-5208	201	18	σ2	σ2	PROPN
ejpam-5208	201	19	)	)	PUNCT
ejpam-5208	201	20	is	be	AUX
ejpam-5208	201	21	(	(	PUNCT
ejpam-5208	201	22	i	i	INTJ
ejpam-5208	201	23	,	,	PUNCT
ejpam-5208	201	24	j)-ψgs	j)-ψgs	ADV
ejpam-5208	201	25	-	-	PUNCT
ejpam-5208	201	26	irresolute	irresolute	ADJ
ejpam-5208	201	27	in	in	ADP
ejpam-5208	201	28	bts	bt	NOUN
ejpam-5208	201	29	if	if	SCONJ
ejpam-5208	201	30	and	and	CCONJ
ejpam-5208	201	31	only	only	ADV
ejpam-5208	201	32	if	if	SCONJ
ejpam-5208	201	33	the	the	DET
ejpam-5208	201	34	inverse	inverse	ADJ
ejpam-5208	201	35	image	image	NOUN
ejpam-5208	201	36	of	of	ADP
ejpam-5208	201	37	every	every	DET
ejpam-5208	201	38	(	(	PUNCT
ejpam-5208	201	39	i	i	NOUN
ejpam-5208	201	40	,	,	PUNCT
ejpam-5208	201	41	j)-ψgs	j)-ψgs	ADV
ejpam-5208	201	42	-	-	ADJ
ejpam-5208	201	43	open	open	ADJ
ejpam-5208	201	44	set	set	NOUN
ejpam-5208	201	45	in	in	ADP
ejpam-5208	201	46	y	y	PROPN
ejpam-5208	201	47	is	be	AUX
ejpam-5208	201	48	a	a	DET
ejpam-5208	201	49	(	(	PUNCT
ejpam-5208	201	50	i	i	NOUN
ejpam-5208	201	51	,	,	PUNCT
ejpam-5208	201	52	j)-ψgs	j)-ψgs	ADV
ejpam-5208	201	53	-	-	ADJ
ejpam-5208	201	54	open	open	ADJ
ejpam-5208	201	55	set	set	NOUN
ejpam-5208	201	56	in	in	ADP
ejpam-5208	201	57	x.	x.	NOUN
ejpam-5208	201	58	proof	proof	NOUN
ejpam-5208	201	59	.	.	PUNCT
ejpam-5208	202	1	let	let	VERB
ejpam-5208	202	2	f	f	PRON
ejpam-5208	202	3	be	be	AUX
ejpam-5208	202	4	(	(	PUNCT
ejpam-5208	202	5	i	i	NOUN
ejpam-5208	202	6	,	,	PUNCT
ejpam-5208	202	7	j)-ψgs	j)-ψgs	ADV
ejpam-5208	202	8	-	-	PUNCT
ejpam-5208	202	9	irresolute	irresolute	ADJ
ejpam-5208	202	10	function	function	NOUN
ejpam-5208	202	11	and	and	CCONJ
ejpam-5208	202	12	let	let	VERB
ejpam-5208	202	13	h	h	PRON
ejpam-5208	202	14	be	be	AUX
ejpam-5208	202	15	(	(	PUNCT
ejpam-5208	202	16	i	i	NOUN
ejpam-5208	202	17	,	,	PUNCT
ejpam-5208	202	18	j)-ψgs	j)-ψgs	ADV
ejpam-5208	202	19	-	-	ADJ
ejpam-5208	202	20	open	open	ADJ
ejpam-5208	202	21	set	set	NOUN
ejpam-5208	202	22	in	in	ADP
ejpam-5208	202	23	y	y	PROPN
ejpam-5208	202	24	.	.	PUNCT
ejpam-5208	203	1	then	then	ADV
ejpam-5208	203	2	y	y	PROPN
ejpam-5208	203	3	∖h	∖h	PROPN
ejpam-5208	203	4	is	be	AUX
ejpam-5208	203	5	(	(	PUNCT
ejpam-5208	203	6	i	i	NOUN
ejpam-5208	203	7	,	,	PUNCT
ejpam-5208	203	8	j)-ψgs	j)-ψgs	ADV
ejpam-5208	203	9	-	-	PUNCT
ejpam-5208	203	10	closed	closed	ADJ
ejpam-5208	203	11	set	set	NOUN
ejpam-5208	203	12	in	in	ADP
ejpam-5208	203	13	y	y	PROPN
ejpam-5208	203	14	.	.	PUNCT
ejpam-5208	204	1	by	by	ADP
ejpam-5208	204	2	assumption	assumption	NOUN
ejpam-5208	204	3	,	,	PUNCT
ejpam-5208	204	4	f−1(y	f−1(y	PROPN
ejpam-5208	204	5	∖h	∖h	NOUN
ejpam-5208	204	6	)	)	PUNCT
ejpam-5208	204	7	=	=	PUNCT
ejpam-5208	204	8	x∖f−1(h	x∖f−1(h	NOUN
ejpam-5208	204	9	)	)	PUNCT
ejpam-5208	204	10	is	be	AUX
ejpam-5208	204	11	(	(	PUNCT
ejpam-5208	204	12	i	i	INTJ
ejpam-5208	204	13	,	,	PUNCT
ejpam-5208	204	14	j)-ψgs	j)-ψgs	ADV
ejpam-5208	204	15	-	-	PUNCT
ejpam-5208	204	16	closed	closed	ADJ
ejpam-5208	204	17	in	in	ADP
ejpam-5208	204	18	x.	x.	NOUN
ejpam-5208	204	19	hence	hence	ADV
ejpam-5208	204	20	,	,	PUNCT
ejpam-5208	204	21	f−1(h	f−1(h	PROPN
ejpam-5208	204	22	)	)	PUNCT
ejpam-5208	204	23	is	be	AUX
ejpam-5208	204	24	(	(	PUNCT
ejpam-5208	204	25	i	i	INTJ
ejpam-5208	204	26	,	,	PUNCT
ejpam-5208	204	27	j)-ψgs	j)-ψgs	ADV
ejpam-5208	204	28	-	-	ADJ
ejpam-5208	204	29	open	open	ADJ
ejpam-5208	204	30	set	set	NOUN
ejpam-5208	204	31	in	in	ADP
ejpam-5208	204	32	x.	x.	NOUN
ejpam-5208	204	33	conversely	conversely	ADV
ejpam-5208	204	34	,	,	PUNCT
ejpam-5208	204	35	let	let	VERB
ejpam-5208	204	36	b	b	X
ejpam-5208	204	37	be	be	AUX
ejpam-5208	204	38	(	(	PUNCT
ejpam-5208	204	39	i	i	NOUN
ejpam-5208	204	40	,	,	PUNCT
ejpam-5208	204	41	j)-ψgs	j)-ψgs	ADV
ejpam-5208	204	42	-	-	PUNCT
ejpam-5208	204	43	closed	closed	ADJ
ejpam-5208	204	44	set	set	NOUN
ejpam-5208	204	45	in	in	ADP
ejpam-5208	204	46	y	y	PROPN
ejpam-5208	204	47	.	.	PUNCT
ejpam-5208	205	1	then	then	ADV
ejpam-5208	205	2	,	,	PUNCT
ejpam-5208	205	3	y∖b	y∖b	PROPN
ejpam-5208	205	4	is	be	AUX
ejpam-5208	205	5	(	(	PUNCT
ejpam-5208	205	6	i	i	NOUN
ejpam-5208	205	7	,	,	PUNCT
ejpam-5208	205	8	j)-ψgs	j)-ψgs	ADV
ejpam-5208	205	9	-	-	ADJ
ejpam-5208	205	10	open	open	ADJ
ejpam-5208	205	11	set	set	NOUN
ejpam-5208	205	12	in	in	ADP
ejpam-5208	205	13	y	y	PROPN
ejpam-5208	205	14	.	.	PUNCT
ejpam-5208	206	1	since	since	SCONJ
ejpam-5208	206	2	the	the	DET
ejpam-5208	206	3	inverse	inverse	NOUN
ejpam-5208	206	4	image	image	NOUN
ejpam-5208	206	5	of	of	ADP
ejpam-5208	206	6	every	every	DET
ejpam-5208	206	7	(	(	PUNCT
ejpam-5208	206	8	i	i	NOUN
ejpam-5208	206	9	,	,	PUNCT
ejpam-5208	206	10	j)-ψgs	j)-ψgs	ADV
ejpam-5208	206	11	-	-	ADJ
ejpam-5208	206	12	open	open	ADJ
ejpam-5208	206	13	set	set	NOUN
ejpam-5208	206	14	in	in	ADP
ejpam-5208	206	15	y	y	PROPN
ejpam-5208	206	16	is	be	AUX
ejpam-5208	206	17	a	a	DET
ejpam-5208	206	18	(	(	PUNCT
ejpam-5208	206	19	i	i	NOUN
ejpam-5208	206	20	,	,	PUNCT
ejpam-5208	206	21	j)-ψgs	j)-ψgs	ADV
ejpam-5208	206	22	-	-	ADJ
ejpam-5208	206	23	open	open	ADJ
ejpam-5208	206	24	set	set	NOUN
ejpam-5208	206	25	in	in	ADP
ejpam-5208	206	26	x	x	PROPN
ejpam-5208	206	27	,	,	PUNCT
ejpam-5208	206	28	f−1(y	f−1(y	PROPN
ejpam-5208	206	29	∖b	∖b	X
ejpam-5208	206	30	)	)	PUNCT
ejpam-5208	206	31	=	=	SYM
ejpam-5208	206	32	x∖f−1(b	x∖f−1(b	X
ejpam-5208	206	33	)	)	PUNCT
ejpam-5208	206	34	is	be	AUX
ejpam-5208	206	35	(	(	PUNCT
ejpam-5208	206	36	i	i	INTJ
ejpam-5208	206	37	,	,	PUNCT
ejpam-5208	206	38	j)-ψgs	j)-ψgs	ADV
ejpam-5208	206	39	-	-	PUNCT
ejpam-5208	206	40	open	open	ADJ
ejpam-5208	206	41	in	in	ADP
ejpam-5208	206	42	x.	x.	PROPN
ejpam-5208	206	43	thus	thus	ADV
ejpam-5208	206	44	,	,	PUNCT
ejpam-5208	206	45	f−1(b	f−1(b	PROPN
ejpam-5208	206	46	)	)	PUNCT
ejpam-5208	206	47	is	be	AUX
ejpam-5208	206	48	(	(	PUNCT
ejpam-5208	206	49	i	i	INTJ
ejpam-5208	206	50	,	,	PUNCT
ejpam-5208	206	51	j)-ψgs	j)-ψgs	ADV
ejpam-5208	206	52	-	-	PUNCT
ejpam-5208	206	53	closed	closed	ADJ
ejpam-5208	206	54	in	in	ADP
ejpam-5208	206	55	x	x	NOUN
ejpam-5208	206	56	,	,	PUNCT
ejpam-5208	206	57	consequently	consequently	ADV
ejpam-5208	206	58	,	,	PUNCT
ejpam-5208	206	59	f	f	PROPN
ejpam-5208	206	60	is	be	AUX
ejpam-5208	206	61	(	(	PUNCT
ejpam-5208	206	62	i	i	PROPN
ejpam-5208	206	63	,	,	PUNCT
ejpam-5208	206	64	j)ψgs	j)ψgs	PROPN
ejpam-5208	206	65	-	-	PUNCT
ejpam-5208	206	66	irresolute	irresolute	ADJ
ejpam-5208	206	67	function	function	NOUN
ejpam-5208	206	68	.	.	PUNCT
ejpam-5208	207	1	theorem	theorem	VERB
ejpam-5208	207	2	13	13	NUM
ejpam-5208	207	3	.	.	PUNCT
ejpam-5208	208	1	let	let	VERB
ejpam-5208	208	2	(	(	PUNCT
ejpam-5208	208	3	x	x	NOUN
ejpam-5208	208	4	,	,	PUNCT
ejpam-5208	208	5	τ1	τ1	NOUN
ejpam-5208	208	6	,	,	PUNCT
ejpam-5208	208	7	τ2	τ2	NOUN
ejpam-5208	208	8	)	)	PUNCT
ejpam-5208	208	9	and	and	CCONJ
ejpam-5208	208	10	(	(	PUNCT
ejpam-5208	208	11	y	y	PROPN
ejpam-5208	208	12	,	,	PUNCT
ejpam-5208	208	13	σ1	σ1	PROPN
ejpam-5208	208	14	,	,	PUNCT
ejpam-5208	208	15	σ2	σ2	PROPN
ejpam-5208	208	16	)	)	PUNCT
ejpam-5208	208	17	be	be	VERB
ejpam-5208	208	18	two	two	NUM
ejpam-5208	208	19	bitopological	bitopological	ADJ
ejpam-5208	208	20	spaces	space	NOUN
ejpam-5208	208	21	.	.	PUNCT
ejpam-5208	209	1	if	if	SCONJ
ejpam-5208	209	2	a	a	DET
ejpam-5208	209	3	function	function	NOUN
ejpam-5208	209	4	f	f	X
ejpam-5208	209	5	:	:	PUNCT
ejpam-5208	209	6	(	(	PUNCT
ejpam-5208	209	7	x	x	NOUN
ejpam-5208	209	8	,	,	PUNCT
ejpam-5208	209	9	τ1	τ1	NOUN
ejpam-5208	209	10	,	,	PUNCT
ejpam-5208	209	11	τ2	τ2	NOUN
ejpam-5208	209	12	)	)	PUNCT
ejpam-5208	209	13	→	→	SYM
ejpam-5208	209	14	(	(	PUNCT
ejpam-5208	209	15	y	y	PROPN
ejpam-5208	209	16	,	,	PUNCT
ejpam-5208	209	17	σ1	σ1	PROPN
ejpam-5208	209	18	,	,	PUNCT
ejpam-5208	209	19	σ2	σ2	PROPN
ejpam-5208	209	20	)	)	PUNCT
ejpam-5208	209	21	is	be	AUX
ejpam-5208	209	22	(	(	PUNCT
ejpam-5208	209	23	i	i	INTJ
ejpam-5208	209	24	,	,	PUNCT
ejpam-5208	209	25	j)-ψgs	j)-ψgs	ADV
ejpam-5208	209	26	-	-	PUNCT
ejpam-5208	209	27	irresolute	irresolute	ADJ
ejpam-5208	209	28	,	,	PUNCT
ejpam-5208	209	29	then	then	ADV
ejpam-5208	209	30	f	f	PROPN
ejpam-5208	209	31	is	be	AUX
ejpam-5208	209	32	(	(	PUNCT
ejpam-5208	209	33	i	i	NOUN
ejpam-5208	209	34	,	,	PUNCT
ejpam-5208	209	35	j)-ψgs	j)-ψgs	ADV
ejpam-5208	209	36	-	-	ADJ
ejpam-5208	209	37	continuous	continuous	ADJ
ejpam-5208	209	38	.	.	PUNCT
ejpam-5208	210	1	l.	l.	PROPN
ejpam-5208	210	2	m.	m.	PROPN
ejpam-5208	210	3	tutanes	tutane	NOUN
ejpam-5208	210	4	/	/	SYM
ejpam-5208	210	5	eur	eur	PROPN
ejpam-5208	210	6	.	.	PUNCT
ejpam-5208	211	1	j.	j.	PROPN
ejpam-5208	211	2	pure	pure	PROPN
ejpam-5208	211	3	appl	appl	PROPN
ejpam-5208	211	4	.	.	PROPN
ejpam-5208	211	5	math	math	PROPN
ejpam-5208	211	6	,	,	PUNCT
ejpam-5208	211	7	17	17	NUM
ejpam-5208	211	8	(	(	PUNCT
ejpam-5208	211	9	3	3	NUM
ejpam-5208	211	10	)	)	PUNCT
ejpam-5208	211	11	(	(	PUNCT
ejpam-5208	211	12	2024	2024	NUM
ejpam-5208	211	13	)	)	PUNCT
ejpam-5208	211	14	,	,	PUNCT
ejpam-5208	211	15	2173	2173	NUM
ejpam-5208	211	16	-	-	SYM
ejpam-5208	211	17	2181	2181	NUM
ejpam-5208	211	18	2180	2180	NUM
ejpam-5208	211	19	proof	proof	NOUN
ejpam-5208	211	20	.	.	PUNCT
ejpam-5208	212	1	let	let	VERB
ejpam-5208	212	2	f	f	PRON
ejpam-5208	212	3	be	be	AUX
ejpam-5208	212	4	(	(	PUNCT
ejpam-5208	212	5	i	i	NOUN
ejpam-5208	212	6	,	,	PUNCT
ejpam-5208	212	7	j)-ψgs	j)-ψgs	ADV
ejpam-5208	212	8	-	-	PUNCT
ejpam-5208	212	9	irresolute	irresolute	ADJ
ejpam-5208	212	10	function	function	NOUN
ejpam-5208	212	11	and	and	CCONJ
ejpam-5208	212	12	a	a	DET
ejpam-5208	212	13	be	be	AUX
ejpam-5208	212	14	σi	σi	NOUN
ejpam-5208	212	15	-	-	PUNCT
ejpam-5208	212	16	closed	close	VERB
ejpam-5208	212	17	set	set	NOUN
ejpam-5208	212	18	in	in	ADP
ejpam-5208	212	19	y	y	PROPN
ejpam-5208	212	20	.	.	PUNCT
ejpam-5208	213	1	by	by	ADP
ejpam-5208	213	2	corollary	corollary	ADJ
ejpam-5208	213	3	1	1	NUM
ejpam-5208	213	4	,	,	PUNCT
ejpam-5208	213	5	a	a	PRON
ejpam-5208	213	6	is	be	AUX
ejpam-5208	213	7	(	(	PUNCT
ejpam-5208	213	8	i	i	PROPN
ejpam-5208	213	9	,	,	PUNCT
ejpam-5208	213	10	j)-ψgs	j)-ψgs	ADV
ejpam-5208	213	11	-	-	PUNCT
ejpam-5208	213	12	closed	closed	ADJ
ejpam-5208	213	13	set	set	NOUN
ejpam-5208	213	14	in	in	ADP
ejpam-5208	213	15	y	y	PROPN
ejpam-5208	213	16	.	.	PUNCT
ejpam-5208	214	1	since	since	SCONJ
ejpam-5208	214	2	f	f	PROPN
ejpam-5208	214	3	is	be	AUX
ejpam-5208	214	4	(	(	PUNCT
ejpam-5208	214	5	i	i	NOUN
ejpam-5208	214	6	,	,	PUNCT
ejpam-5208	214	7	j)-ψgs	j)-ψgs	ADV
ejpam-5208	214	8	-	-	PUNCT
ejpam-5208	214	9	irresolute	irresolute	ADJ
ejpam-5208	214	10	function	function	NOUN
ejpam-5208	214	11	,	,	PUNCT
ejpam-5208	214	12	f−1(a	f−1(a	PROPN
ejpam-5208	214	13	)	)	PUNCT
ejpam-5208	214	14	is	be	AUX
ejpam-5208	214	15	(	(	PUNCT
ejpam-5208	214	16	i	i	X
ejpam-5208	214	17	,	,	PUNCT
ejpam-5208	214	18	j)ψgs	j)ψgs	PROPN
ejpam-5208	214	19	-	-	PUNCT
ejpam-5208	214	20	closed	close	VERB
ejpam-5208	214	21	set	set	NOUN
ejpam-5208	214	22	in	in	ADP
ejpam-5208	214	23	x.	x.	NOUN
ejpam-5208	214	24	therefore	therefore	ADV
ejpam-5208	214	25	,	,	PUNCT
ejpam-5208	214	26	f	f	PROPN
ejpam-5208	214	27	is	be	AUX
ejpam-5208	214	28	(	(	PUNCT
ejpam-5208	214	29	i	i	NOUN
ejpam-5208	214	30	,	,	PUNCT
ejpam-5208	214	31	j)-ψgs	j)-ψgs	ADV
ejpam-5208	214	32	-	-	ADJ
ejpam-5208	214	33	continuous	continuous	ADJ
ejpam-5208	214	34	.	.	PUNCT
ejpam-5208	215	1	theorem	theorem	VERB
ejpam-5208	215	2	14	14	NUM
ejpam-5208	215	3	.	.	PUNCT
ejpam-5208	216	1	if	if	SCONJ
ejpam-5208	216	2	f	f	PROPN
ejpam-5208	216	3	:	:	PUNCT
ejpam-5208	216	4	(	(	PUNCT
ejpam-5208	216	5	x	x	NOUN
ejpam-5208	216	6	,	,	PUNCT
ejpam-5208	216	7	τ1	τ1	NOUN
ejpam-5208	216	8	,	,	PUNCT
ejpam-5208	216	9	τ2	τ2	NOUN
ejpam-5208	216	10	)	)	PUNCT
ejpam-5208	216	11	→	→	SYM
ejpam-5208	216	12	(	(	PUNCT
ejpam-5208	216	13	y	y	PROPN
ejpam-5208	216	14	,	,	PUNCT
ejpam-5208	216	15	σ1	σ1	PROPN
ejpam-5208	216	16	,	,	PUNCT
ejpam-5208	216	17	σ2	σ2	NOUN
ejpam-5208	216	18	)	)	PUNCT
ejpam-5208	216	19	and	and	CCONJ
ejpam-5208	216	20	g	g	NOUN
ejpam-5208	216	21	:	:	PUNCT
ejpam-5208	216	22	(	(	PUNCT
ejpam-5208	216	23	y	y	PROPN
ejpam-5208	216	24	,	,	PUNCT
ejpam-5208	216	25	σ1	σ1	PROPN
ejpam-5208	216	26	,	,	PUNCT
ejpam-5208	216	27	σ2	σ2	NOUN
ejpam-5208	216	28	)	)	PUNCT
ejpam-5208	216	29	→	→	SYM
ejpam-5208	216	30	(	(	PUNCT
ejpam-5208	216	31	z	z	NOUN
ejpam-5208	216	32	,	,	PUNCT
ejpam-5208	216	33	µ1	µ1	PROPN
ejpam-5208	216	34	,	,	PUNCT
ejpam-5208	216	35	µ2	µ2	PROPN
ejpam-5208	216	36	)	)	PUNCT
ejpam-5208	216	37	are	be	AUX
ejpam-5208	216	38	(	(	PUNCT
ejpam-5208	216	39	i	i	X
ejpam-5208	216	40	,	,	PUNCT
ejpam-5208	216	41	j)ψgs	j)ψgs	PROPN
ejpam-5208	216	42	-	-	PUNCT
ejpam-5208	216	43	irresolute	irresolute	ADJ
ejpam-5208	216	44	functions	function	NOUN
ejpam-5208	216	45	,	,	PUNCT
ejpam-5208	216	46	then	then	ADV
ejpam-5208	216	47	g	g	PROPN
ejpam-5208	216	48	◦	◦	NOUN
ejpam-5208	217	1	f	f	X
ejpam-5208	217	2	:	:	PUNCT
ejpam-5208	217	3	(	(	PUNCT
ejpam-5208	217	4	x	x	NOUN
ejpam-5208	217	5	,	,	PUNCT
ejpam-5208	217	6	τ1	τ1	NOUN
ejpam-5208	217	7	,	,	PUNCT
ejpam-5208	217	8	τ2	τ2	NOUN
ejpam-5208	217	9	)	)	PUNCT
ejpam-5208	217	10	→	→	SYM
ejpam-5208	217	11	(	(	PUNCT
ejpam-5208	217	12	z	z	NOUN
ejpam-5208	217	13	,	,	PUNCT
ejpam-5208	217	14	µ1	µ1	PROPN
ejpam-5208	217	15	,	,	PUNCT
ejpam-5208	217	16	µ2	µ2	PROPN
ejpam-5208	217	17	)	)	PUNCT
ejpam-5208	217	18	is	be	AUX
ejpam-5208	217	19	(	(	PUNCT
ejpam-5208	217	20	i	i	INTJ
ejpam-5208	217	21	,	,	PUNCT
ejpam-5208	217	22	j)-ψgs	j)-ψgs	ADV
ejpam-5208	217	23	-	-	PUNCT
ejpam-5208	217	24	irresolute	irresolute	ADJ
ejpam-5208	217	25	.	.	PUNCT
ejpam-5208	218	1	proof	proof	NOUN
ejpam-5208	218	2	.	.	PUNCT
ejpam-5208	219	1	let	let	VERB
ejpam-5208	219	2	a	a	DET
ejpam-5208	219	3	be	be	AUX
ejpam-5208	219	4	(	(	PUNCT
ejpam-5208	219	5	i	i	NOUN
ejpam-5208	219	6	,	,	PUNCT
ejpam-5208	219	7	j)-ψgs	j)-ψgs	ADV
ejpam-5208	219	8	-	-	PUNCT
ejpam-5208	219	9	closed	closed	ADJ
ejpam-5208	219	10	set	set	NOUN
ejpam-5208	219	11	in	in	ADP
ejpam-5208	219	12	z.	z.	PROPN
ejpam-5208	219	13	since	since	SCONJ
ejpam-5208	219	14	g	g	PROPN
ejpam-5208	219	15	is	be	AUX
ejpam-5208	219	16	(	(	PUNCT
ejpam-5208	219	17	i	i	NOUN
ejpam-5208	219	18	,	,	PUNCT
ejpam-5208	219	19	j)-ψgs	j)-ψgs	ADV
ejpam-5208	219	20	-	-	PUNCT
ejpam-5208	219	21	irresolute	irresolute	ADJ
ejpam-5208	219	22	function	function	NOUN
ejpam-5208	219	23	,	,	PUNCT
ejpam-5208	219	24	g−1(a	g−1(a	PROPN
ejpam-5208	219	25	)	)	PUNCT
ejpam-5208	219	26	is	be	AUX
ejpam-5208	219	27	(	(	PUNCT
ejpam-5208	219	28	i	i	INTJ
ejpam-5208	219	29	,	,	PUNCT
ejpam-5208	219	30	j)-ψgs	j)-ψgs	ADV
ejpam-5208	219	31	-	-	PUNCT
ejpam-5208	219	32	closed	closed	ADJ
ejpam-5208	219	33	set	set	NOUN
ejpam-5208	219	34	in	in	ADP
ejpam-5208	219	35	y	y	PROPN
ejpam-5208	219	36	.	.	PUNCT
ejpam-5208	220	1	moreover	moreover	ADV
ejpam-5208	220	2	,	,	PUNCT
ejpam-5208	220	3	f−1(g−1(a	f−1(g−1(a	PROPN
ejpam-5208	220	4	)	)	PUNCT
ejpam-5208	220	5	)	)	PUNCT
ejpam-5208	220	6	is	be	AUX
ejpam-5208	220	7	(	(	PUNCT
ejpam-5208	220	8	i	i	INTJ
ejpam-5208	220	9	,	,	PUNCT
ejpam-5208	220	10	j)-ψgs	j)-ψgs	ADV
ejpam-5208	220	11	-	-	PUNCT
ejpam-5208	220	12	closed	closed	ADJ
ejpam-5208	220	13	set	set	NOUN
ejpam-5208	220	14	in	in	ADP
ejpam-5208	220	15	x	x	PUNCT
ejpam-5208	220	16	since	since	SCONJ
ejpam-5208	220	17	f	f	PROPN
ejpam-5208	220	18	is	be	AUX
ejpam-5208	220	19	(	(	PUNCT
ejpam-5208	220	20	i	i	NOUN
ejpam-5208	220	21	,	,	PUNCT
ejpam-5208	220	22	j)-ψgs	j)-ψgs	ADV
ejpam-5208	220	23	-	-	PUNCT
ejpam-5208	220	24	irresolute	irresolute	ADJ
ejpam-5208	220	25	function	function	NOUN
ejpam-5208	220	26	.	.	PUNCT
ejpam-5208	221	1	note	note	VERB
ejpam-5208	221	2	that	that	SCONJ
ejpam-5208	221	3	(	(	PUNCT
ejpam-5208	221	4	g	g	PROPN
ejpam-5208	221	5	◦	◦	NOUN
ejpam-5208	221	6	f)−1(a	f)−1(a	NOUN
ejpam-5208	221	7	)	)	PUNCT
ejpam-5208	222	1	=	=	SYM
ejpam-5208	222	2	f−1(g−1(a	f−1(g−1(a	PROPN
ejpam-5208	222	3	)	)	PUNCT
ejpam-5208	222	4	)	)	PUNCT
ejpam-5208	222	5	.	.	PUNCT
ejpam-5208	223	1	therefore	therefore	ADV
ejpam-5208	223	2	,	,	PUNCT
ejpam-5208	223	3	g	g	PROPN
ejpam-5208	223	4	◦	◦	NOUN
ejpam-5208	223	5	f	f	X
ejpam-5208	223	6	is	be	AUX
ejpam-5208	223	7	(	(	PUNCT
ejpam-5208	223	8	i	i	NOUN
ejpam-5208	223	9	,	,	PUNCT
ejpam-5208	223	10	j)-ψgs	j)-ψgs	ADV
ejpam-5208	223	11	-	-	PUNCT
ejpam-5208	223	12	irresolute	irresolute	ADJ
ejpam-5208	223	13	.	.	PUNCT
ejpam-5208	224	1	theorem	theorem	NOUN
ejpam-5208	224	2	15	15	NUM
ejpam-5208	224	3	.	.	PUNCT
ejpam-5208	225	1	if	if	SCONJ
ejpam-5208	225	2	f	f	PROPN
ejpam-5208	225	3	:	:	PUNCT
ejpam-5208	225	4	(	(	PUNCT
ejpam-5208	225	5	x	x	NOUN
ejpam-5208	225	6	,	,	PUNCT
ejpam-5208	225	7	τ1	τ1	NOUN
ejpam-5208	225	8	,	,	PUNCT
ejpam-5208	225	9	τ2	τ2	NOUN
ejpam-5208	225	10	)	)	PUNCT
ejpam-5208	225	11	→	→	SYM
ejpam-5208	225	12	(	(	PUNCT
ejpam-5208	225	13	y	y	PROPN
ejpam-5208	225	14	,	,	PUNCT
ejpam-5208	225	15	σ1	σ1	PROPN
ejpam-5208	225	16	,	,	PUNCT
ejpam-5208	225	17	σ2	σ2	NOUN
ejpam-5208	225	18	)	)	PUNCT
ejpam-5208	225	19	and	and	CCONJ
ejpam-5208	225	20	g	g	NOUN
ejpam-5208	225	21	:	:	PUNCT
ejpam-5208	225	22	(	(	PUNCT
ejpam-5208	225	23	y	y	PROPN
ejpam-5208	225	24	,	,	PUNCT
ejpam-5208	225	25	σ1	σ1	PROPN
ejpam-5208	225	26	,	,	PUNCT
ejpam-5208	225	27	σ2	σ2	NOUN
ejpam-5208	225	28	)	)	PUNCT
ejpam-5208	225	29	→	→	SYM
ejpam-5208	225	30	(	(	PUNCT
ejpam-5208	225	31	z	z	NOUN
ejpam-5208	225	32	,	,	PUNCT
ejpam-5208	225	33	µ1	µ1	PROPN
ejpam-5208	225	34	,	,	PUNCT
ejpam-5208	225	35	µ2	µ2	PROPN
ejpam-5208	225	36	)	)	PUNCT
ejpam-5208	225	37	are	be	AUX
ejpam-5208	225	38	(	(	PUNCT
ejpam-5208	225	39	i	i	X
ejpam-5208	225	40	,	,	PUNCT
ejpam-5208	225	41	j)ψgs	j)ψgs	PROPN
ejpam-5208	225	42	-	-	PUNCT
ejpam-5208	225	43	irresolute	irresolute	ADJ
ejpam-5208	225	44	functions	function	NOUN
ejpam-5208	225	45	,	,	PUNCT
ejpam-5208	225	46	then	then	ADV
ejpam-5208	225	47	g	g	PROPN
ejpam-5208	225	48	◦	◦	NOUN
ejpam-5208	226	1	f	f	X
ejpam-5208	226	2	:	:	PUNCT
ejpam-5208	226	3	(	(	PUNCT
ejpam-5208	226	4	x	x	NOUN
ejpam-5208	226	5	,	,	PUNCT
ejpam-5208	226	6	τ1	τ1	NOUN
ejpam-5208	226	7	,	,	PUNCT
ejpam-5208	226	8	τ2	τ2	NOUN
ejpam-5208	226	9	)	)	PUNCT
ejpam-5208	226	10	→	→	SYM
ejpam-5208	226	11	(	(	PUNCT
ejpam-5208	226	12	z	z	NOUN
ejpam-5208	226	13	,	,	PUNCT
ejpam-5208	226	14	µ1	µ1	PROPN
ejpam-5208	226	15	,	,	PUNCT
ejpam-5208	226	16	µ2	µ2	PROPN
ejpam-5208	226	17	)	)	PUNCT
ejpam-5208	226	18	is	be	AUX
ejpam-5208	226	19	(	(	PUNCT
ejpam-5208	226	20	i	i	NOUN
ejpam-5208	226	21	,	,	PUNCT
ejpam-5208	226	22	j)-ψgs	j)-ψgs	ADV
ejpam-5208	226	23	-	-	ADJ
ejpam-5208	226	24	continuous	continuous	ADJ
ejpam-5208	226	25	.	.	PUNCT
ejpam-5208	227	1	proof	proof	NOUN
ejpam-5208	227	2	.	.	PUNCT
ejpam-5208	228	1	let	let	VERB
ejpam-5208	228	2	b	b	X
ejpam-5208	228	3	be	be	AUX
ejpam-5208	228	4	µi	µi	ADV
ejpam-5208	228	5	-	-	PUNCT
ejpam-5208	228	6	closed	close	VERB
ejpam-5208	228	7	set	set	NOUN
ejpam-5208	228	8	in	in	ADP
ejpam-5208	228	9	z.	z.	PROPN
ejpam-5208	228	10	by	by	ADP
ejpam-5208	228	11	corollary	corollary	ADJ
ejpam-5208	228	12	1	1	NUM
ejpam-5208	228	13	,	,	PUNCT
ejpam-5208	228	14	b	b	NOUN
ejpam-5208	228	15	is	be	AUX
ejpam-5208	228	16	(	(	PUNCT
ejpam-5208	228	17	i	i	NOUN
ejpam-5208	228	18	,	,	PUNCT
ejpam-5208	228	19	j)-ψgs	j)-ψgs	ADV
ejpam-5208	228	20	-	-	PUNCT
ejpam-5208	228	21	closed	closed	ADJ
ejpam-5208	228	22	set	set	NOUN
ejpam-5208	228	23	in	in	ADP
ejpam-5208	228	24	z.	z.	PROPN
ejpam-5208	228	25	since	since	SCONJ
ejpam-5208	228	26	g	g	PROPN
ejpam-5208	228	27	is	be	AUX
ejpam-5208	228	28	(	(	PUNCT
ejpam-5208	228	29	i	i	NOUN
ejpam-5208	228	30	,	,	PUNCT
ejpam-5208	228	31	j)-ψgs	j)-ψgs	ADV
ejpam-5208	228	32	-	-	PUNCT
ejpam-5208	228	33	irresolute	irresolute	ADJ
ejpam-5208	228	34	function	function	NOUN
ejpam-5208	228	35	,	,	PUNCT
ejpam-5208	228	36	g−1(b	g−1(b	PROPN
ejpam-5208	228	37	)	)	PUNCT
ejpam-5208	228	38	is	be	AUX
ejpam-5208	228	39	(	(	PUNCT
ejpam-5208	228	40	i	i	INTJ
ejpam-5208	228	41	,	,	PUNCT
ejpam-5208	228	42	j)-ψgs	j)-ψgs	ADV
ejpam-5208	228	43	-	-	PUNCT
ejpam-5208	228	44	closed	closed	ADJ
ejpam-5208	228	45	set	set	NOUN
ejpam-5208	228	46	in	in	ADP
ejpam-5208	228	47	y	y	PROPN
ejpam-5208	228	48	.	.	PUNCT
ejpam-5208	229	1	also	also	ADV
ejpam-5208	229	2	,	,	PUNCT
ejpam-5208	229	3	since	since	SCONJ
ejpam-5208	229	4	f	f	PROPN
ejpam-5208	229	5	is	be	AUX
ejpam-5208	229	6	(	(	PUNCT
ejpam-5208	229	7	i	i	NOUN
ejpam-5208	229	8	,	,	PUNCT
ejpam-5208	229	9	j)-ψgs	j)-ψgs	ADV
ejpam-5208	229	10	-	-	PUNCT
ejpam-5208	229	11	irresolute	irresolute	ADJ
ejpam-5208	229	12	function	function	NOUN
ejpam-5208	229	13	,	,	PUNCT
ejpam-5208	229	14	f−1(g−1(b	f−1(g−1(b	PROPN
ejpam-5208	229	15	)	)	PUNCT
ejpam-5208	229	16	)	)	PUNCT
ejpam-5208	230	1	=	=	PRON
ejpam-5208	230	2	(	(	PUNCT
ejpam-5208	230	3	g	g	PROPN
ejpam-5208	230	4	◦	◦	NOUN
ejpam-5208	230	5	f)−1(b	f)−1(b	PROPN
ejpam-5208	230	6	)	)	PUNCT
ejpam-5208	230	7	is	be	AUX
ejpam-5208	230	8	(	(	PUNCT
ejpam-5208	230	9	i	i	INTJ
ejpam-5208	230	10	,	,	PUNCT
ejpam-5208	230	11	j)-ψgs	j)-ψgs	ADV
ejpam-5208	230	12	-	-	PUNCT
ejpam-5208	230	13	closed	closed	ADJ
ejpam-5208	230	14	set	set	NOUN
ejpam-5208	230	15	in	in	ADP
ejpam-5208	230	16	x.	x.	NOUN
ejpam-5208	230	17	therefore	therefore	ADV
ejpam-5208	230	18	,	,	PUNCT
ejpam-5208	230	19	g	g	PROPN
ejpam-5208	230	20	◦	◦	NOUN
ejpam-5208	230	21	f	f	X
ejpam-5208	230	22	is	be	AUX
ejpam-5208	230	23	(	(	PUNCT
ejpam-5208	230	24	i	i	NOUN
ejpam-5208	230	25	,	,	PUNCT
ejpam-5208	230	26	j)-ψgs	j)-ψgs	ADV
ejpam-5208	230	27	-	-	ADJ
ejpam-5208	230	28	continuous	continuous	ADJ
ejpam-5208	230	29	.	.	PUNCT
ejpam-5208	231	1	theorem	theorem	VERB
ejpam-5208	231	2	16	16	NUM
ejpam-5208	231	3	.	.	PUNCT
ejpam-5208	232	1	if	if	SCONJ
ejpam-5208	232	2	a	a	DET
ejpam-5208	232	3	function	function	NOUN
ejpam-5208	232	4	f	f	X
ejpam-5208	232	5	:	:	PUNCT
ejpam-5208	232	6	(	(	PUNCT
ejpam-5208	232	7	x	x	NOUN
ejpam-5208	232	8	,	,	PUNCT
ejpam-5208	232	9	τ1	τ1	NOUN
ejpam-5208	232	10	,	,	PUNCT
ejpam-5208	232	11	τ2	τ2	NOUN
ejpam-5208	232	12	)	)	PUNCT
ejpam-5208	232	13	→	→	SYM
ejpam-5208	232	14	(	(	PUNCT
ejpam-5208	232	15	y	y	PROPN
ejpam-5208	232	16	,	,	PUNCT
ejpam-5208	232	17	σ1	σ1	PROPN
ejpam-5208	232	18	,	,	PUNCT
ejpam-5208	232	19	σ2	σ2	PROPN
ejpam-5208	232	20	)	)	PUNCT
ejpam-5208	232	21	is	be	AUX
ejpam-5208	232	22	(	(	PUNCT
ejpam-5208	232	23	i	i	INTJ
ejpam-5208	232	24	,	,	PUNCT
ejpam-5208	232	25	j)-ψgs	j)-ψgs	ADV
ejpam-5208	232	26	-	-	PUNCT
ejpam-5208	232	27	irresolute	irresolute	ADJ
ejpam-5208	232	28	function	function	NOUN
ejpam-5208	232	29	and	and	CCONJ
ejpam-5208	232	30	g	g	NOUN
ejpam-5208	232	31	:	:	PUNCT
ejpam-5208	232	32	(	(	PUNCT
ejpam-5208	232	33	y	y	PROPN
ejpam-5208	232	34	,	,	PUNCT
ejpam-5208	232	35	σ1	σ1	PROPN
ejpam-5208	232	36	,	,	PUNCT
ejpam-5208	232	37	σ2	σ2	NOUN
ejpam-5208	232	38	)	)	PUNCT
ejpam-5208	232	39	→	→	SYM
ejpam-5208	232	40	(	(	PUNCT
ejpam-5208	232	41	z	z	NOUN
ejpam-5208	232	42	,	,	PUNCT
ejpam-5208	232	43	µ1	µ1	PROPN
ejpam-5208	232	44	,	,	PUNCT
ejpam-5208	232	45	µ2	µ2	PROPN
ejpam-5208	232	46	)	)	PUNCT
ejpam-5208	232	47	is	be	AUX
ejpam-5208	232	48	(	(	PUNCT
ejpam-5208	232	49	i	i	INTJ
ejpam-5208	232	50	,	,	PUNCT
ejpam-5208	232	51	j)-ψgs	j)-ψgs	ADV
ejpam-5208	232	52	-	-	ADJ
ejpam-5208	232	53	continuous	continuous	ADJ
ejpam-5208	232	54	function	function	NOUN
ejpam-5208	232	55	,	,	PUNCT
ejpam-5208	232	56	then	then	ADV
ejpam-5208	232	57	g	g	PROPN
ejpam-5208	232	58	◦	◦	NOUN
ejpam-5208	233	1	f	f	X
ejpam-5208	233	2	:	:	PUNCT
ejpam-5208	233	3	(	(	PUNCT
ejpam-5208	233	4	x	x	NOUN
ejpam-5208	233	5	,	,	PUNCT
ejpam-5208	233	6	τ1	τ1	NOUN
ejpam-5208	233	7	,	,	PUNCT
ejpam-5208	233	8	τ2	τ2	NOUN
ejpam-5208	233	9	)	)	PUNCT
ejpam-5208	233	10	→	→	SYM
ejpam-5208	233	11	(	(	PUNCT
ejpam-5208	233	12	z	z	NOUN
ejpam-5208	233	13	,	,	PUNCT
ejpam-5208	233	14	µ1	µ1	PROPN
ejpam-5208	233	15	,	,	PUNCT
ejpam-5208	233	16	µ2	µ2	PROPN
ejpam-5208	233	17	)	)	PUNCT
ejpam-5208	233	18	is	be	AUX
ejpam-5208	233	19	(	(	PUNCT
ejpam-5208	233	20	i	i	NOUN
ejpam-5208	233	21	,	,	PUNCT
ejpam-5208	233	22	j)-ψgs	j)-ψgs	ADV
ejpam-5208	233	23	-	-	ADJ
ejpam-5208	233	24	continuous	continuous	ADJ
ejpam-5208	233	25	.	.	PUNCT
ejpam-5208	234	1	proof	proof	NOUN
ejpam-5208	234	2	.	.	PUNCT
ejpam-5208	235	1	let	let	VERB
ejpam-5208	235	2	v	v	PART
ejpam-5208	235	3	be	be	AUX
ejpam-5208	235	4	µi	µi	ADV
ejpam-5208	235	5	-	-	PUNCT
ejpam-5208	235	6	closed	close	VERB
ejpam-5208	235	7	set	set	NOUN
ejpam-5208	235	8	in	in	ADP
ejpam-5208	235	9	z.	z.	PROPN
ejpam-5208	235	10	then	then	ADV
ejpam-5208	235	11	g−1(v	g−1(v	PROPN
ejpam-5208	235	12	)	)	PUNCT
ejpam-5208	236	1	is	be	AUX
ejpam-5208	236	2	(	(	PUNCT
ejpam-5208	236	3	i	i	INTJ
ejpam-5208	236	4	,	,	PUNCT
ejpam-5208	236	5	j)-ψgs	j)-ψgs	ADV
ejpam-5208	236	6	-	-	PUNCT
ejpam-5208	236	7	closed	closed	ADJ
ejpam-5208	236	8	set	set	NOUN
ejpam-5208	236	9	in	in	ADP
ejpam-5208	236	10	y	y	PROPN
ejpam-5208	236	11	since	since	SCONJ
ejpam-5208	236	12	g	g	PROPN
ejpam-5208	236	13	is	be	AUX
ejpam-5208	236	14	(	(	PUNCT
ejpam-5208	236	15	i	i	INTJ
ejpam-5208	236	16	,	,	PUNCT
ejpam-5208	236	17	j)-ψgs	j)-ψgs	ADV
ejpam-5208	236	18	-	-	ADJ
ejpam-5208	236	19	continuous	continuous	ADJ
ejpam-5208	236	20	function	function	NOUN
ejpam-5208	236	21	.	.	PUNCT
ejpam-5208	237	1	it	it	PRON
ejpam-5208	237	2	follows	follow	VERB
ejpam-5208	237	3	that	that	PRON
ejpam-5208	237	4	f−1(g−1(v	f−1(g−1(v	PROPN
ejpam-5208	237	5	)	)	PUNCT
ejpam-5208	237	6	)	)	PUNCT
ejpam-5208	238	1	=	=	PRON
ejpam-5208	238	2	(	(	PUNCT
ejpam-5208	238	3	g	g	NOUN
ejpam-5208	238	4	◦	◦	NOUN
ejpam-5208	238	5	f)−1(v	f)−1(v	NOUN
ejpam-5208	238	6	)	)	PUNCT
ejpam-5208	238	7	is	be	AUX
ejpam-5208	238	8	(	(	PUNCT
ejpam-5208	238	9	i	i	X
ejpam-5208	238	10	,	,	PUNCT
ejpam-5208	238	11	j)ψgs	j)ψgs	PROPN
ejpam-5208	238	12	-	-	PUNCT
ejpam-5208	238	13	closed	close	VERB
ejpam-5208	238	14	set	set	NOUN
ejpam-5208	238	15	in	in	ADP
ejpam-5208	238	16	x	x	PUNCT
ejpam-5208	238	17	since	since	SCONJ
ejpam-5208	238	18	f	f	PROPN
ejpam-5208	238	19	is	be	AUX
ejpam-5208	238	20	(	(	PUNCT
ejpam-5208	238	21	i	i	NOUN
ejpam-5208	238	22	,	,	PUNCT
ejpam-5208	238	23	j)-ψgs	j)-ψgs	ADV
ejpam-5208	238	24	-	-	PUNCT
ejpam-5208	238	25	irresolute	irresolute	ADJ
ejpam-5208	238	26	function	function	NOUN
ejpam-5208	238	27	.	.	PUNCT
ejpam-5208	239	1	therefore	therefore	ADV
ejpam-5208	239	2	,	,	PUNCT
ejpam-5208	239	3	g	g	PROPN
ejpam-5208	239	4	◦	◦	NOUN
ejpam-5208	239	5	f	f	X
ejpam-5208	239	6	is	be	AUX
ejpam-5208	239	7	(	(	PUNCT
ejpam-5208	239	8	i	i	NOUN
ejpam-5208	239	9	,	,	PUNCT
ejpam-5208	239	10	j)-ψgscontinuous	j)-ψgscontinuous	ADJ
ejpam-5208	239	11	.	.	PUNCT
ejpam-5208	240	1	7	7	X
ejpam-5208	240	2	.	.	X
ejpam-5208	240	3	conclusion	conclusion	NOUN
ejpam-5208	240	4	in	in	ADP
ejpam-5208	240	5	this	this	DET
ejpam-5208	240	6	paper	paper	NOUN
ejpam-5208	240	7	,	,	PUNCT
ejpam-5208	240	8	the	the	DET
ejpam-5208	240	9	author	author	NOUN
ejpam-5208	240	10	defined	define	VERB
ejpam-5208	240	11	and	and	CCONJ
ejpam-5208	240	12	introduced	introduce	VERB
ejpam-5208	240	13	(	(	PUNCT
ejpam-5208	240	14	i	i	NOUN
ejpam-5208	240	15	,	,	PUNCT
ejpam-5208	240	16	j)-ψgs	j)-ψgs	ADV
ejpam-5208	240	17	-	-	PUNCT
ejpam-5208	240	18	open	open	ADJ
ejpam-5208	241	1	and	and	CCONJ
ejpam-5208	241	2	(	(	PUNCT
ejpam-5208	241	3	i	i	NOUN
ejpam-5208	241	4	,	,	PUNCT
ejpam-5208	241	5	j)-ψgs	j)-ψgs	ADV
ejpam-5208	241	6	-	-	PUNCT
ejpam-5208	241	7	closed	close	VERB
ejpam-5208	241	8	functions	function	NOUN
ejpam-5208	241	9	,	,	PUNCT
ejpam-5208	241	10	(	(	PUNCT
ejpam-5208	241	11	i	i	INTJ
ejpam-5208	241	12	,	,	PUNCT
ejpam-5208	241	13	j)-ψgs	j)-ψgs	ADV
ejpam-5208	241	14	-	-	PUNCT
ejpam-5208	241	15	continuous	continuous	ADJ
ejpam-5208	241	16	functions	function	NOUN
ejpam-5208	241	17	,	,	PUNCT
ejpam-5208	241	18	and	and	CCONJ
ejpam-5208	241	19	(	(	PUNCT
ejpam-5208	241	20	i	i	NOUN
ejpam-5208	241	21	,	,	PUNCT
ejpam-5208	241	22	j)-ψgs	j)-ψgs	ADV
ejpam-5208	241	23	-	-	PUNCT
ejpam-5208	241	24	irresolute	irresolute	ADJ
ejpam-5208	241	25	functions	function	NOUN
ejpam-5208	241	26	using	use	VERB
ejpam-5208	241	27	(	(	PUNCT
ejpam-5208	241	28	i	i	PROPN
ejpam-5208	241	29	,	,	PUNCT
ejpam-5208	241	30	j)ψgs	j)ψgs	PROPN
ejpam-5208	241	31	-	-	PUNCT
ejpam-5208	241	32	closed	close	VERB
ejpam-5208	241	33	sets	set	NOUN
ejpam-5208	241	34	in	in	ADP
ejpam-5208	241	35	bitopological	bitopological	ADJ
ejpam-5208	241	36	spaces	space	NOUN
ejpam-5208	241	37	.	.	PUNCT
ejpam-5208	242	1	the	the	DET
ejpam-5208	242	2	properties	property	NOUN
ejpam-5208	242	3	and	and	CCONJ
ejpam-5208	242	4	characterizations	characterization	NOUN
ejpam-5208	242	5	of	of	ADP
ejpam-5208	242	6	these	these	DET
ejpam-5208	242	7	functions	function	NOUN
ejpam-5208	242	8	were	be	AUX
ejpam-5208	242	9	investigated	investigate	VERB
ejpam-5208	242	10	in	in	ADP
ejpam-5208	242	11	detail	detail	NOUN
ejpam-5208	242	12	.	.	PUNCT
ejpam-5208	243	1	the	the	DET
ejpam-5208	243	2	results	result	NOUN
ejpam-5208	243	3	of	of	ADP
ejpam-5208	243	4	this	this	DET
ejpam-5208	243	5	study	study	NOUN
ejpam-5208	243	6	are	be	AUX
ejpam-5208	243	7	purely	purely	ADV
ejpam-5208	243	8	theoretical	theoretical	ADJ
ejpam-5208	243	9	;	;	PUNCT
ejpam-5208	243	10	therefore	therefore	ADV
ejpam-5208	243	11	,	,	PUNCT
ejpam-5208	243	12	further	further	ADJ
ejpam-5208	243	13	research	research	NOUN
ejpam-5208	243	14	into	into	ADP
ejpam-5208	243	15	the	the	DET
ejpam-5208	243	16	practical	practical	ADJ
ejpam-5208	243	17	applications	application	NOUN
ejpam-5208	243	18	of	of	ADP
ejpam-5208	243	19	these	these	DET
ejpam-5208	243	20	findings	finding	NOUN
ejpam-5208	243	21	is	be	AUX
ejpam-5208	243	22	recommended	recommend	VERB
ejpam-5208	243	23	.	.	PUNCT
ejpam-5208	244	1	acknowledgements	acknowledgement	NOUN
ejpam-5208	244	2	the	the	DET
ejpam-5208	244	3	author	author	NOUN
ejpam-5208	244	4	expresses	express	VERB
ejpam-5208	244	5	gratitude	gratitude	NOUN
ejpam-5208	244	6	to	to	ADP
ejpam-5208	244	7	the	the	DET
ejpam-5208	244	8	bukidnon	bukidnon	NOUN
ejpam-5208	244	9	state	state	PROPN
ejpam-5208	244	10	university	university	PROPN
ejpam-5208	244	11	center	center	NOUN
ejpam-5208	244	12	of	of	ADP
ejpam-5208	244	13	mathematical	mathematical	ADJ
ejpam-5208	244	14	innovations	innovation	NOUN
ejpam-5208	244	15	for	for	ADP
ejpam-5208	244	16	their	their	PRON
ejpam-5208	244	17	financial	financial	ADJ
ejpam-5208	244	18	support	support	NOUN
ejpam-5208	244	19	.	.	PUNCT
ejpam-5208	245	1	references	reference	NOUN
ejpam-5208	245	2	2181	2181	NUM
ejpam-5208	245	3	references	reference	NOUN
ejpam-5208	245	4	[	[	X
ejpam-5208	245	5	1	1	NUM
ejpam-5208	245	6	]	]	X
ejpam-5208	245	7	a.n	a.n	PROPN
ejpam-5208	245	8	.	.	PROPN
ejpam-5208	245	9	atewi	atewi	PROPN
ejpam-5208	245	10	,	,	PUNCT
ejpam-5208	245	11	b.s	b.s	PROPN
ejpam-5208	245	12	.	.	PROPN
ejpam-5208	245	13	naser	naser	PROPN
ejpam-5208	245	14	,	,	PUNCT
ejpam-5208	245	15	s.j	s.j	PROPN
ejpam-5208	245	16	.	.	PROPN
ejpam-5208	245	17	ali	ali	PROPN
ejpam-5208	245	18	,	,	PUNCT
ejpam-5208	245	19	and	and	CCONJ
ejpam-5208	245	20	m.a	m.a	PROPN
ejpam-5208	245	21	.	.	PROPN
ejpam-5208	245	22	harhoosh	harhoosh	PROPN
ejpam-5208	245	23	.	.	PUNCT
ejpam-5208	246	1	forms	form	NOUN
ejpam-5208	246	2	of	of	ADP
ejpam-5208	246	3	ω	ω	NUM
ejpam-5208	246	4	-continuous	-continuous	ADJ
ejpam-5208	246	5	functions	function	NOUN
ejpam-5208	246	6	between	between	ADP
ejpam-5208	246	7	bitopological	bitopological	ADJ
ejpam-5208	246	8	spaces	space	NOUN
ejpam-5208	246	9	.	.	PUNCT
ejpam-5208	247	1	int	int	NOUN
ejpam-5208	247	2	.	.	PUNCT
ejpam-5208	248	1	j.	j.	PROPN
ejpam-5208	248	2	nonlinear	nonlinear	PROPN
ejpam-5208	248	3	anal	anal	PROPN
ejpam-5208	248	4	.	.	PUNCT
ejpam-5208	249	1	appl	appl	PROPN
ejpam-5208	249	2	.	.	PROPN
ejpam-5208	249	3	,	,	PUNCT
ejpam-5208	249	4	13(1):2219–2225	13(1):2219–2225	NUM
ejpam-5208	249	5	,	,	PUNCT
ejpam-5208	249	6	2022	2022	NUM
ejpam-5208	249	7	.	.	PUNCT
ejpam-5208	250	1	[	[	X
ejpam-5208	250	2	2	2	X
ejpam-5208	250	3	]	]	PUNCT
ejpam-5208	250	4	s.	s.	PROPN
ejpam-5208	250	5	kadham	kadham	PROPN
ejpam-5208	250	6	and	and	CCONJ
ejpam-5208	250	7	h.	h.	PROPN
ejpam-5208	250	8	hassan	hassan	PROPN
ejpam-5208	250	9	.	.	PUNCT
ejpam-5208	251	1	on	on	ADP
ejpam-5208	251	2	λ	λ	ADJ
ejpam-5208	251	3	-	-	ADJ
ejpam-5208	251	4	continuous	continuous	ADJ
ejpam-5208	251	5	function	function	NOUN
ejpam-5208	251	6	.	.	PUNCT
ejpam-5208	252	1	babylon	babylon	PROPN
ejpam-5208	252	2	university	university	PROPN
ejpam-5208	252	3	,	,	PUNCT
ejpam-5208	252	4	13	13	NUM
ejpam-5208	252	5	,	,	PUNCT
ejpam-5208	252	6	2009	2009	NUM
ejpam-5208	252	7	.	.	PUNCT
ejpam-5208	253	1	[	[	X
ejpam-5208	253	2	3	3	NUM
ejpam-5208	253	3	]	]	X
ejpam-5208	253	4	f.h	f.h	PROPN
ejpam-5208	253	5	.	.	PROPN
ejpam-5208	253	6	khedr	khedr	PROPN
ejpam-5208	253	7	and	and	CCONJ
ejpam-5208	253	8	h.s	h.s	PROPN
ejpam-5208	253	9	.	.	PROPN
ejpam-5208	253	10	al	al	PROPN
ejpam-5208	253	11	-	-	PUNCT
ejpam-5208	253	12	saadi	saadi	NOUN
ejpam-5208	253	13	.	.	PUNCT
ejpam-5208	254	1	generalized	generalize	VERB
ejpam-5208	254	2	semi	semi	ADJ
ejpam-5208	254	3	-	-	ADJ
ejpam-5208	254	4	closed	closed	ADJ
ejpam-5208	254	5	functions	function	NOUN
ejpam-5208	254	6	and	and	CCONJ
ejpam-5208	254	7	semigeneralized	semigeneralize	VERB
ejpam-5208	254	8	closed	closed	ADJ
ejpam-5208	254	9	functions	function	NOUN
ejpam-5208	254	10	in	in	ADP
ejpam-5208	254	11	bitopological	bitopological	ADJ
ejpam-5208	254	12	spaces	space	NOUN
ejpam-5208	254	13	.	.	PUNCT
ejpam-5208	255	1	journal	journal	NOUN
ejpam-5208	255	2	of	of	ADP
ejpam-5208	255	3	the	the	DET
ejpam-5208	255	4	egyptian	egyptian	PROPN
ejpam-5208	255	5	mathematical	mathematical	PROPN
ejpam-5208	255	6	society	society	NOUN
ejpam-5208	255	7	,	,	PUNCT
ejpam-5208	255	8	20:14–19	20:14–19	PROPN
ejpam-5208	255	9	,	,	PUNCT
ejpam-5208	255	10	2012	2012	NUM
ejpam-5208	255	11	.	.	PUNCT
ejpam-5208	256	1	[	[	X
ejpam-5208	256	2	4	4	X
ejpam-5208	256	3	]	]	PUNCT
ejpam-5208	256	4	s.	s.	PROPN
ejpam-5208	256	5	mahmood	mahmood	PROPN
ejpam-5208	256	6	and	and	CCONJ
ejpam-5208	256	7	s.	s.	PROPN
ejpam-5208	256	8	hamdi	hamdi	PROPN
ejpam-5208	256	9	.	.	PUNCT
ejpam-5208	257	1	on	on	ADP
ejpam-5208	257	2	(	(	PUNCT
ejpam-5208	257	3	1	1	NUM
ejpam-5208	257	4	,	,	PUNCT
ejpam-5208	257	5	2)∗	2)∗	NOUN
ejpam-5208	257	6	b	b	X
ejpam-5208	257	7	-	-	PUNCT
ejpam-5208	257	8	open	open	ADJ
ejpam-5208	257	9	functions	function	NOUN
ejpam-5208	257	10	and	and	CCONJ
ejpam-5208	257	11	(	(	PUNCT
ejpam-5208	257	12	1	1	NUM
ejpam-5208	257	13	,	,	PUNCT
ejpam-5208	257	14	2)∗b	2)∗b	NUM
ejpam-5208	257	15	-	-	PUNCT
ejpam-5208	257	16	closed	close	VERB
ejpam-5208	257	17	functions	function	NOUN
ejpam-5208	257	18	i	i	PRON
ejpam-5208	257	19	bitopological	bitopological	ADJ
ejpam-5208	257	20	spaces	space	NOUN
ejpam-5208	257	21	.	.	PUNCT
ejpam-5208	258	1	journal	journal	PROPN
ejpam-5208	258	2	of	of	ADP
ejpam-5208	258	3	al	al	PROPN
ejpam-5208	258	4	-	-	PUNCT
ejpam-5208	258	5	nahrain	nahrain	PROPN
ejpam-5208	258	6	university	university	NOUN
ejpam-5208	258	7	science	science	NOUN
ejpam-5208	258	8	,	,	PUNCT
ejpam-5208	258	9	17(1):73–79	17(1):73–79	NUM
ejpam-5208	258	10	,	,	PUNCT
ejpam-5208	258	11	2014	2014	NUM
ejpam-5208	258	12	.	.	PUNCT
ejpam-5208	259	1	[	[	X
ejpam-5208	259	2	5	5	NUM
ejpam-5208	259	3	]	]	X
ejpam-5208	259	4	a.j	a.j	PROPN
ejpam-5208	259	5	.	.	PROPN
ejpam-5208	259	6	moosa	moosa	PROPN
ejpam-5208	259	7	meera	meera	PROPN
ejpam-5208	259	8	,	,	PUNCT
ejpam-5208	259	9	n.m	n.m	PROPN
ejpam-5208	259	10	.	.	PROPN
ejpam-5208	259	11	abbas	abbas	PROPN
ejpam-5208	259	12	,	,	PUNCT
ejpam-5208	259	13	and	and	CCONJ
ejpam-5208	260	1	s.a	s.a	PROPN
ejpam-5208	260	2	.	.	PROPN
ejpam-5208	260	3	al	al	PROPN
ejpam-5208	260	4	-	-	PUNCT
ejpam-5208	260	5	hadi	hadi	PROPN
ejpam-5208	260	6	.	.	PUNCT
ejpam-5208	261	1	on	on	ADP
ejpam-5208	261	2	weaklyλ	weaklyλ	NOUN
ejpam-5208	261	3	-	-	PUNCT
ejpam-5208	261	4	continous	continous	ADJ
ejpam-5208	261	5	functions	function	NOUN
ejpam-5208	261	6	in	in	ADP
ejpam-5208	261	7	bitopological	bitopological	ADJ
ejpam-5208	261	8	spaces	space	NOUN
ejpam-5208	261	9	.	.	PUNCT
ejpam-5208	262	1	journal	journal	PROPN
ejpam-5208	262	2	of	of	ADP
ejpam-5208	262	3	kerbala	kerbala	PROPN
ejpam-5208	262	4	university	university	PROPN
ejpam-5208	262	5	,	,	PUNCT
ejpam-5208	262	6	10(3):325–327	10(3):325–327	NOUN
ejpam-5208	262	7	,	,	PUNCT
ejpam-5208	262	8	2012	2012	NUM
ejpam-5208	262	9	.	.	PUNCT
ejpam-5208	263	1	[	[	X
ejpam-5208	263	2	6	6	NUM
ejpam-5208	263	3	]	]	X
ejpam-5208	263	4	c.	c.	PROPN
ejpam-5208	263	5	mukundhan	mukundhan	PROPN
ejpam-5208	263	6	and	and	CCONJ
ejpam-5208	263	7	n.	n.	PROPN
ejpam-5208	263	8	nagaveni	nagaveni	PROPN
ejpam-5208	263	9	.	.	PUNCT
ejpam-5208	264	1	(	(	PUNCT
ejpam-5208	264	2	i	i	NOUN
ejpam-5208	264	3	,	,	PUNCT
ejpam-5208	264	4	j)-quasi	j)-quasi	DET
ejpam-5208	264	5	semi	semi	ADJ
ejpam-5208	264	6	weakly	weakly	ADV
ejpam-5208	264	7	g∗-closed	g∗-close	VERB
ejpam-5208	264	8	functions	function	NOUN
ejpam-5208	264	9	in	in	ADP
ejpam-5208	264	10	bitopological	bitopological	ADJ
ejpam-5208	264	11	spaces	space	NOUN
ejpam-5208	264	12	.	.	PUNCT
ejpam-5208	265	1	international	international	ADJ
ejpam-5208	265	2	journal	journal	PROPN
ejpam-5208	265	3	of	of	ADP
ejpam-5208	265	4	computer	computer	NOUN
ejpam-5208	265	5	science	science	NOUN
ejpam-5208	265	6	issues	issue	NOUN
ejpam-5208	265	7	,	,	PUNCT
ejpam-5208	265	8	9(2):469	9(2):469	NUM
ejpam-5208	265	9	–	–	PUNCT
ejpam-5208	265	10	474	474	NUM
ejpam-5208	265	11	,	,	PUNCT
ejpam-5208	265	12	2012	2012	NUM
ejpam-5208	265	13	.	.	PUNCT
ejpam-5208	266	1	[	[	X
ejpam-5208	266	2	7	7	X
ejpam-5208	266	3	]	]	PUNCT
ejpam-5208	266	4	t.	t.	PROPN
ejpam-5208	266	5	noiri	noiri	PROPN
ejpam-5208	266	6	and	and	CCONJ
ejpam-5208	266	7	v.	v.	ADP
ejpam-5208	266	8	popa	popa	NOUN
ejpam-5208	266	9	.	.	PUNCT
ejpam-5208	267	1	some	some	DET
ejpam-5208	267	2	properties	property	NOUN
ejpam-5208	267	3	of	of	ADP
ejpam-5208	267	4	weakly	weakly	ADJ
ejpam-5208	267	5	open	open	ADJ
ejpam-5208	267	6	functions	function	NOUN
ejpam-5208	267	7	in	in	ADP
ejpam-5208	267	8	bitopologcal	bitopologcal	ADJ
ejpam-5208	267	9	spaces	space	NOUN
ejpam-5208	267	10	.	.	PUNCT
ejpam-5208	268	1	novi	novi	PROPN
ejpam-5208	268	2	sad	sad	PROPN
ejpam-5208	268	3	j.	j.	PROPN
ejpam-5208	268	4	math	math	PROPN
ejpam-5208	268	5	,	,	PUNCT
ejpam-5208	268	6	36(1):47–54	36(1):47–54	NUM
ejpam-5208	268	7	,	,	PUNCT
ejpam-5208	268	8	2006	2006	NUM
ejpam-5208	268	9	.	.	PUNCT
ejpam-5208	269	1	[	[	X
ejpam-5208	269	2	8	8	NUM
ejpam-5208	269	3	]	]	X
ejpam-5208	269	4	s.t	s.t	PROPN
ejpam-5208	269	5	.	.	PROPN
ejpam-5208	269	6	leevathi	leevathi	PROPN
ejpam-5208	269	7	s.	s.	PROPN
ejpam-5208	269	8	sivanthi	sivanthi	PROPN
ejpam-5208	269	9	.	.	PUNCT
ejpam-5208	270	1	on	on	ADP
ejpam-5208	270	2	τ1τ2rg	τ1τ2rg	NOUN
ejpam-5208	270	3	-	-	PUNCT
ejpam-5208	270	4	continuous	continuous	ADJ
ejpam-5208	270	5	in	in	ADP
ejpam-5208	270	6	bitopological	bitopological	ADJ
ejpam-5208	270	7	spaces	space	NOUN
ejpam-5208	270	8	andτ1τ2rgirresolute	andτ1τ2rgirresolute	NOUN
ejpam-5208	270	9	functions	function	NOUN
ejpam-5208	270	10	.	.	PUNCT
ejpam-5208	271	1	ijcrt	ijcrt	NOUN
ejpam-5208	271	2	,	,	PUNCT
ejpam-5208	271	3	9(1):1164–1168	9(1):1164–1168	PROPN
ejpam-5208	271	4	,	,	PUNCT
ejpam-5208	271	5	2021	2021	NUM
ejpam-5208	271	6	.	.	PUNCT
ejpam-5208	272	1	[	[	X
ejpam-5208	272	2	9	9	NUM
ejpam-5208	272	3	]	]	X
ejpam-5208	272	4	d.j	d.j	PROPN
ejpam-5208	272	5	.	.	PROPN
ejpam-5208	272	6	sarma	sarma	PROPN
ejpam-5208	272	7	.	.	PUNCT
ejpam-5208	273	1	weakly	weakly	ADJ
ejpam-5208	273	2	b	b	X
ejpam-5208	273	3	-	-	PUNCT
ejpam-5208	273	4	open	open	ADJ
ejpam-5208	273	5	functions	function	NOUN
ejpam-5208	273	6	in	in	ADP
ejpam-5208	273	7	bitopological	bitopological	ADJ
ejpam-5208	273	8	spaces	space	NOUN
ejpam-5208	273	9	.	.	PUNCT
ejpam-5208	274	1	bol	bol	NOUN
ejpam-5208	274	2	.	.	PUNCT
ejpam-5208	275	1	soc	soc	PROPN
ejpam-5208	275	2	.	.	PUNCT
ejpam-5208	276	1	paran	paran	PROPN
ejpam-5208	276	2	.	.	PUNCT
ejpam-5208	277	1	mat	mat	PROPN
ejpam-5208	277	2	.	.	PROPN
ejpam-5208	277	3	,	,	PUNCT
ejpam-5208	277	4	35(2):105–114	35(2):105–114	PROPN
ejpam-5208	277	5	,	,	PUNCT
ejpam-5208	277	6	2017	2017	NUM
ejpam-5208	277	7	.	.	PUNCT
ejpam-5208	278	1	[	[	X
ejpam-5208	278	2	10	10	NUM
ejpam-5208	278	3	]	]	X
ejpam-5208	278	4	s.	s.	PROPN
ejpam-5208	278	5	tahiliani	tahiliani	PROPN
ejpam-5208	278	6	.	.	PUNCT
ejpam-5208	279	1	on	on	ADP
ejpam-5208	279	2	weakly	weakly	ADJ
ejpam-5208	279	3	β	β	ADJ
ejpam-5208	279	4	-	-	ADJ
ejpam-5208	279	5	continuous	continuous	ADJ
ejpam-5208	279	6	function	function	NOUN
ejpam-5208	279	7	in	in	ADP
ejpam-5208	279	8	bitopological	bitopological	ADJ
ejpam-5208	279	9	spaces	space	NOUN
ejpam-5208	279	10	.	.	PUNCT
ejpam-5208	280	1	filomat	filomat	NOUN
ejpam-5208	280	2	,	,	PUNCT
ejpam-5208	280	3	22(1):77–86	22(1):77–86	NUM
ejpam-5208	280	4	,	,	PUNCT
ejpam-5208	280	5	2008	2008	NUM
ejpam-5208	280	6	.	.	PUNCT
ejpam-5208	281	1	[	[	X
ejpam-5208	281	2	11	11	NUM
ejpam-5208	281	3	]	]	X
ejpam-5208	281	4	l.m	l.m	PROPN
ejpam-5208	281	5	.	.	PROPN
ejpam-5208	281	6	tutanes	tutane	NOUN
ejpam-5208	281	7	.	.	PUNCT
ejpam-5208	282	1	on	on	ADP
ejpam-5208	282	2	ψgs	ψgs	ADV
ejpam-5208	282	3	-	-	PUNCT
ejpam-5208	282	4	closed	close	VERB
ejpam-5208	282	5	sets	set	NOUN
ejpam-5208	282	6	in	in	ADP
ejpam-5208	282	7	bitopological	bitopological	ADJ
ejpam-5208	282	8	spaces	space	NOUN
ejpam-5208	282	9	.	.	PUNCT
ejpam-5208	283	1	european	european	ADJ
ejpam-5208	283	2	journal	journal	PROPN
ejpam-5208	283	3	of	of	ADP
ejpam-5208	283	4	pure	pure	ADJ
ejpam-5208	283	5	and	and	CCONJ
ejpam-5208	283	6	applied	applied	ADJ
ejpam-5208	283	7	mathematics	mathematic	NOUN
ejpam-5208	283	8	,	,	PUNCT
ejpam-5208	283	9	14(4):1275–1282	14(4):1275–1282	NUM
ejpam-5208	283	10	,	,	PUNCT
ejpam-5208	283	11	2021	2021	NUM
ejpam-5208	283	12	.	.	PUNCT